Mick Galwey's Shannon did not have it their own way as 'Wegians proved doughty opponents, against a side which beat them 34-9 over 12 months ago.
Having edged the first half 9-3, thanks to two penalties and a 19th minute drop goal from David Delaney, Shannon's defence lapsed on 55 minutes.
By that time Delaney had struck another neat drop, but Bernie Kelly's side kept in the hunt when number eight Scott Donald brilliantly charged down a Delaney clearance kick to beat John Lacey for the touch down.
Shannon regrouped at 12-10 in front, and almost immediately got in for their second try. Back row Quinlan sniped blindside off a scrum 30 metres out, and with Stephen Keogh ensuring second phase ball, scrum-half Fiach O'Loughlin recycled for Quinlan to sprint over.
Delaney and Cleary kicked two penalties each in the closing minutes before left wing McLoughlin scored on 78 minutes, collecting Delaney's clever chip through.
Up north, Jeremy Davidson's 'Gannon cooked up a Stevenson Park stew for Lansdowne, recording their second win of the season - 13-11 - with Ulster and Ireland wing Tyrone 'T Bone' Howe back in tow.
The 33-year-old beefed up the northerners' backline but it was inside centre skipper Paul Magee who did the damage - scoring the match-winning try on the hour, after the Dubliners had new back row recruit Christian Kos yellow carded.
Davidson hailed his side's tenacity, after they came back from 8-6 down at the break.
"It was a remarkable team performance and it will give us confidence going into the next few weeks," said the former Ireland lock.
"We played the right type of game in the conditions and our defence won the game for us. It was good to put a performance in for 80 minutes as I felt against UCD and Clontarf we had the upper hand for 60 minutes."
Lansdowne hooker Kevin Corrigan had earlier burrowed over following a turnover scrum on 5 minutes - for his second try in successive games.
Clontarf slumped to their first defeat of the season on Saturday, as young Cork Con winger Peter O'Brien - making his first AIL start - scored the only try in a 19-9 home win at Temple Hill.
'Tarf lost John Duffy and Simon O'Donnell to sin-binnings either side of half-time as their challenge waned.
A good start saw former UCD skipper Shane Moore drop a goal, but a searing Cronan Healy break paved the way for O'Brien to touch down on 14 minutes. Con took a 13-6 lead into the second half after Pat McCarthy had kicked two penalties and a conversion to Paul Ryan's sole effort on 34 minutes.
Ryan, filling in for the unavailable Dave McAllister at number 10, kicked a second on 50 minutes, but 13-9 was as close as it got as Barry Keeshan tagged on a penalty and drop goal to Con's tally, maintaining their record of just one defeat in their last ten home outings.
Cork Constitution 19 Clontarf 9, Temple HillScorers: Cork: Try: O'Brien; Con: McCarthy; Pens: McCarthy 2, Keeshan; Drop goal: Keeshan
Dungannon 13 Lansdowne 11, Stevenson ParkScorers: Dungannon: Try: Magee; Con: Steenson; Pens: Steenson 2
Galwegians 16 Shannon 28, Crowley ParkScorers: Galwegians: Try: Donald; Con: Cleary; Pens: Cleary 3Shannon: Tries: Quinlan, McLoughlin; Pens: Delaney 4; Drop goals: Delaney 2
Barnhall 7 Waterpark 9Bective Rangers 39 Young Munster 18De La Salle Palmerston 25 Ballynahinch 10Highfield 10 UL Bohemian 27Malone 14 Old Belvedere 26Midleton 11 Dolphin 16Old Crescent 15 Thomond 9UCC 42 Terenure 13
Ards 34 Old Wesley 25Ballina 7 City of Derry 23Bruff 17 Corinthians 22Connemara 37 Portadown 7Greystones 43 Clonakilty 11Sunday's Well 33 Wanderers 16Suttonians 18 Queen's University 6