The ex-Galwegians kicker's haul pushed Mick Galwey's side back to the top of AIB League Division One, despite the Braidmen scoring two late tries.
Delaney, who kicked 41 points in his previous three games, converted just one of Shannon's four tries - hooker Nigel Conroy's 30th-minute opener - but also pocketed an opportunist drop goal and two penalties, with Ulster starlet Paddy Wallace in direct opposition.
The forward battle was immense with Ulster loosehead Bryan Young scoring five minutes before the break, only to see Shannon fullback David O'Donovan slalom through for his second try in the space of a week - cruelly robbing the Braidmen's attack on his own 22, and racing to the right corner in a brilliant breakaway move.
18-10 up at half-time, a Fionn McLoughlin effort and a stolen lineout maul over from prop Tony Buckley saw Shannon power clear. Former Ulster Under-21 Andrew Trimble twice - with his first on 57 minutes a crafty chip-collect - and Matt Waterhouse kept Steph Nel's lot in the hunt, but the damage was already done.
Garryowen made it a Limerick one-two at the summit, as Paul Cunningham's side got back on the rails with a 27-18 defeat of Buccaneers at Dubarry Park.
Once again a number 10 won the game outright - Alan Purcell grabbing 14 points, as he kicked three second half penalties and thundered over in the left corner on 84 minutes to summon up the light Blues' fifth win of the campaign. Buccs' Adrian Hanley and former Athlone skipper Marcus Madden shared out the other tries with free-scoring Garryowen centre Ray Niland.
Two Conor Kilroy penalties and a Shane Madigan try, created by Owen Cullen's lineout steal, helped Blackrock College to a vital 13-8 win at former leaders Clontarf.
'Tarf's Dave Hewitt kept the home side in the hunt at 13-5 down at the break, with his effort coming from a deflected hack on by Donovan Rossi, but all Phil Werahiko's men could offer in defence of a two-game unbeaten home run, in the second half, was a 50th-minute Darragh O'Shea penalty. Niall O'Brien was also denied a late try due to a foot-in-touch.
Saturday was finally County Carlow's day as, at the fourth attempt, they prized away a home win - beating Dungannon 26-14 - at Oak Park, and moving off bottom spot.
Tries from Padraig Brennan and Andy Meville in either half, and 16 points from fit-again fly-half Richie Murphy - whose four early penalties aided Ray Ward's men towards a 19-3 break lead - saw the northerners downed.
Lansdowne hit rock bottom as South African WP Strauss scored Belfast Harlequins' sole try in their 13-9 success. Incredibly it was Quins' fourth consecutive match without conceding a try. Andy Tallon booted three penalties for the home side.
Meanwhile, Sunday saw Leinster Under-21 Stephen Grissing pocket his first AIB League try in his debut season, as previously-unbeaten UCD edged out Galwegians 19-13 at Crowley Park.
The students' Ross McCarron also touched down for his third of the season, with fly-half Eoghan Hickey kicking three penalties to John Cleary's two. 'Wegians centre Stuart Meagher scored their sole try in the second half, as they brought it back to 16-13.
In Division Two, the top two - Dolphin and St Mary's College - finished level at 10-10 in a pulsating tie at Musgrave Park.
The Cork men still hold the edge in first place, two points clear of Mary's, who have a game in hand, with third-placed UCC a further point behind.
Dolphin centre Mick Manning bagged a first half try for a 10-0 home lead, but Mary's flanker Paul Nash struck back on 78 minutes, with John O'Mahony and John Sexton each kicking five points.
A rampant Greystones side chalked up their ninth win of the season in Division Three, as they ran out 21-5 win over newly-promoted Bruff.
Stuart McConnell, David McKechnie and David Popplewell all touched down for the Wicklow men. However, chasers Connemara undoubtedly had the win of the weekend, as they came away from Banbridge with a 32-5 victory.
The westerners' were too good - scoring tries through David Keogh, Fergal Wood, Noel Walshe, Kevin Keogh and John Casey against their Rifle Park hosts - who had been without a fixture for the past four weeks.
AIB League: January 22-23
Ballymena 27 Shannon 31, Eaton ParkBuccaneers 18 Garryowen 27, Dubarry Park
Ballynahinch 16 Thomond 6, Ballymacarn ParkBective Rangers 16 Barnhall 3, DonnybrookDLSP v Highfield, Kilternan (*Postponed)Dolphin 10 St Mary's College 10, Musgrave ParkMidleton 3 Malone 0, Towns ParkOld Belvedere v UL Bohemian, Anglesea Road (*Postponed)Old Crescent 15 Waterpark 0, RosbrienYoung Munster 3 UCC 12, Tom Clifford Park
Banbridge 5 Connemara 32, Rifle ParkBruff 5 Greystones 21, Kilballyowen ParkCity of Derry 22 Suttonians 17, Judges RoadClonakilty 18 Queen's University 7, Shannonvale CrossCorinthians 29 Sundays Well 5, Corinthian ParkInstonians 9 Ards 15, Shaw's BridgePortadown 16 Skerries 17, Chambers ParkWanderers v Lansdowne, Lansdowne Road (*Postponed)