Munster joined the Ospreys at the top of the Celtic League table, having edged Lyn Jones' side thanks to a late try from hooker Sheahan.
His second in successive games handed the points to Alan Gaffney's side, after a quick lineout take by Alan Quinlan, and drive by the Munster forwards.
The Welsh visitors - who had won three of their last four games in all competitions - held a 6-3 half-time lead, despite losing international number eight Ryan Jones to a silly 37th minute red card for a stamp on Donncha O'Callaghan.
Golden-booted centre Gavin Henson drilled over two low efforts in a swirling wind on 12 and 32 minutes, after Ronan O'Gara had opened the scoring in the tenth minute, from 22 metres out.
O'Gara, captaining Munster for the first time, also crept past the 200-point league career mark as he added a second on 50 minutes, after Henson had put the Ospreys 9-3 in front on the restart, and converted Sheahan's maul over effort.
The win - Munster's eighth straight league success - also handed them a psychological advantage ahead of the sides' fourth meeting in 11 months - a Heineken Cup Pool 4 duel at Thomond Park on January 8.
Afterwards, coach Gaffney commented: They were tough conditions, and it was a disappointing game really. We're not happy with what we did, but happy with the win.
A poor lineout meant we were unable to set up our usual platform - both sides coughed up a lot of set piece ball. But we'll get better and we just have to move on and address that.We dominated the second half, played a lot of territory. Fair dues to the Ospreys for playing as they did with 14 men., but the rub of the green probably went their way at times.
(15) Christian Cullen(14) Shaun Payne(13) Mike Mullins(12) Rob Henderson(11) Paul Devlin(10) Ronan O'Gara (Capt)(9) Peter Stringer(1) Marcus Horan(2) Frankie Sheahan(3) Gordon McIlwham(4) Donncha O'Callaghan(5) Tom Bowman(6) Alan Quinlan(7) Denis Leamy(8) Jim Williams
Replacements used:Trevor Hogan for Bowman (64 mins). Not used: Frankie Roche, Jerry Flannery, Stephen Keogh, Eoin Reddan, Paul Burke, James Storey.
Cardiff 6 LEINSTER 15, Arms ParkScorers: Cardiff: Pens: Lee Thomas 2Leinster: Tries: David Quinlan, Girvan Dempsey; Con: Felipe Contepomi; Pen: Contepomi
Ireland international Gordon D'Arcy tasted his first action for 48 days when coming on as a 70th minute substitute in Leinster's 15-6 win over the Cardiff Blues at the Arms Park on Saturday.
The 24-year-old - who suffered a groin strain in October's 30-11 Heineken Cup win over Bath, was medically cleared for a return earlier this week, and had an immediate impact, ending a late 20-metre run with a neat offload for full-back Girvan Dempsey to touch down, and confirm Leinster's fourth win on-the-trot.
It was also a first home loss of the season for the Blues.
Declan Kidney's side moved six points behind league leaders the Ospreys, with another encouraging display, in only their second win on Welsh soil in eleven visits east.
Argentine international Felipe Contepomi took many of the plaudits as he sent lanky centre David Quinlan in for the opening try.
The South American - who ran up his points tally for the last three games to 24, with a first half conversion and penalty - offloaded for Blackrock star Quinlan to touch down under the Blues' posts after only 40 seconds.
He added the extras and a 30-metre penalty, before Lee Thomas kicked his first of two penalties just before the interval for a 10-3 deficit.
The Blues - whose best chance fell short early in the second period through international Martyn Williams - drew back to 10-6 down with Thomas' second kick but Leinster held firm - even without influential international trio Brian O'Driscoll, Denis Hickie and Shane Horgan.
Five minutes from time, D'Arcy, on the field for Gary Brown, evaded some poor tackling from the Cardiff rearguard to pave the way for Dempsey's second try of the season, and confirm Leinster's third place in the table.
With festive derbies against Ulster and second-placed Munster to come, Kidney's charges could have a big say in the destination of this season's Celtic Cup.
(15) Girvan Dempsey(14) John McWeeney(13) Kieran Lewis(12) David Quinlan(11) Gary Brown(10) Felipe Contepomi(9) Guy Easterby(1) Emmett Byrne(2) Shane Byrne(3) Ricky Nebbett(4) Malcolm O'Kelly (Capt)(5) Ben Gissing(6) Aidan McCullen(7) Shane Jennings(8) Eric Miller
ULSTER 36 Edinburgh 34, RavenhillScorers: Ulster: Tries: Kevin Maggs, Rowan Frost, Tommy Bowe, Paul Steinmetz; Cons: Steinmetz 2; Pens: David Humphreys 3, SteinmetzEdinburgh: Tries: Paul Boston, Allister Hogg, Derrick Lee, David Callam; Cons: Brendan Laney 4; Pens: Laney 2
Ulster and Edinburgh duelled out a 70-point thriller - the most points scored in a single game in the league this season - on Friday night at Ravenhill, as New Zealander Paul Steinmetz rescued the spoils for Mark McCall's side with a crucial 12-point haul.
The Kiwi centre - who, along with midfield partner Kevin Maggs, scored an early try for a 13-0 Ulster lead - converted second half efforts from Tommy Bowe and Rowan Frost, and also kicked a penalty after regular fly-half David Humphreys had been forced onto the sidelines with a foot injury.
Edinburgh brought the game back level at half-time (13-13), in front of a Belfast attendance of 5,858, as Paul Boston crossed the whitewash and wily number 10 Brendan Laney tagged on three sure-footed penalties.
Frank Hadden's visitors even led 27-22 for a time in a topsy-turvy game, as both Scotland back row Allister Hogg and full-back Derrick Lee - scoring a record 17th career try in the competition - with Humphreys kicking his second and third penalties.
After Bowe and substitute Frost had helped McCall's charges reassume the lead, Edinburgh's David Callam ensured a tense finale when scoring a converted try on 77 minutes, but nevertheless Ulster held on for their first bonus point victory of the season.
Former Ireland centre McCall said of the victory: That was a very important win for us, but on saying that, I'm not looking forward to watching the video. It was a strange game as we bossed it for the first 25 minutes, scored two good tries, but then switched off and made too many mistakes.
Our defence was as effective as our attack and we kept allowing Edinburgh back into the game.
That was our fourth win from six home games so we are starting to build a bit of form at Ravenhill, he added.
(15) Bryn Cunningham(14) Tommy Bowe(13) Kevin Maggs(12) Paul Steinmetz(11) Tyrone Howe(10) David Humphreys(9) Kieran Campbell(1) Ronan McCormack(2) Paul Shields(3) Rod Moore(4) Gary Longwell(5) Matt McCullough(6) Campbell Feather (Capt)(7) Gavin Pfister(8) Roger Wilson
Replacements used:Rory Best for Shields (44 mins), Simon Best for Moore (50), Rowan Frost for Pfister (67). Not used: Matt Mustchin, Neil Doak, Adam Larkin, Andrew Maxwell.
Glasgow 35 CONNACHT 0, HughendenScorers: Glasgow: Tries: Sean Lamont 2, Kevin Tkachuk, Donnie Macfadyen; Cons: Calvin Howarth 2, Dan Parks; Pens: Howarth 3
Seventh-placed Connacht are just three points ahead of Ulster in the Celtic League table, after they crumbled to a 35-0 loss in Glasgow on Friday night.
A rake of recent injuries and a hectic schedule saw the westerners succumb to their fifth loss of the campaign - with next week's visit of Munster to the Sportsground and New Year's Day's trip to Ravenhill now taking on added importance.
Ireland Under 21 Brendan O'Connor made his league debut, but that was the sole highlight on a disappointing night for coach Michael Bradley, who watched his side outshone by a highflying home outfit.
Calvin Howarth notched three early penalties for the Scots and matters turned further in their favour as Connacht centre Paul Warwick - the scorer of 83 points in his previous ten league games - was sin-binned on 34 minutes for hands in the ruck.
Nifty number 10 Howarth then sent Sean Lamont scampering in at the corner, for his first of two tries and a 14-0 half time lead.
Howarth converted Canada World Cup prop Kevin Tkachuk's 45th minute touch down, and also added the extras to Lamont's second, after Colin Shaw's 30-metre dash.
Hugh Campbell's side had to wait until injury time to confirm their third bonus point of the season, as Scotland flanker Donnie Macfadyen crossed the whitewash for substitute Dan Parks to convert.
The 28-year-old Howarth (84%) leads the league's best kicking stats, with the yellow-carded Warwick (82.86% - 29 successes from 35 attempts) joint-second with Parks.
(15) Matt Mostyn(14) Justin Meagher(13) Paul Warwick(12) James Downey(11) Conor McPhillips(10) Eric Elwood(9) Chris Keane(1) Ray Hogan(2) Bernard Jackman(3) Stephen Knoop(4) Christian Short(5) Andrew Farley (Capt)(6) Michael Swift(7) John Muldoon(8) John O'Sullivan
Replacements used:Brendan O'Connor for O'Sullivan (19-21 mins), Adrian Clarke for Hogan (45-51), John Fogarty for Jackman (50), Tom Tierney for Keane, Niall O'Brien for Elwood (both 50), Pieter Myburgh for Farley (66), O'Connor for Swift (67), Clarke for Knoop (70). Not used: Ted Robinson.
Sin-bin: Paul Warwick (34-44 mins)