A last-gasp try by outhalf Alan Conboy secured a bonus point for St Mary's in an open match that was heavily influenced by the wind.
The more experienced St Mary's side got the better of the weather when they went in at half -time just 13-3 adrift.
And with the wind at their backs the home side gradually wore Buccaneers down.
Scrumhalf Conor McPhilips was at the centre of everything in the second half, and gave outhalf Alan Conboy an excellent service, as St Mary's notched up the points.
Buccaneers started in fine style with a try just five minutes into the game from winger Ted Robinson after some fine scissors passing by Adrian Hanley and John Meagher. Outhalf Colm Glynn added the conversion.
Glynn also added a further penalty and a finely struck drop goal before the interval, but St Mary's were always in charge in difficult playing conditions.
St Mary's got their name on the scoreboard when Conboy slotted an easy penalty before the break from under the posts.
Glynn had a chance to stretch Buccaneers' lead just before the interval after tighthead prop Martin Cahill made a storming run up the field, but the sides crossed over with St Mary's just 10 points adrift.
St Mary's cut their deficit three minutes into the second half. After a huge overdrive from a lineout prop Dave Clare touched down for a try that was converted by Conboy.
The sides were level shortly afterwards, courtesy of a penalty from Conboy, and after that St Mary's never looked back.
The Jennings brothers, playing at number seven and eight, pounced on any loose ball going and Karl Jennings was rewarded by a try midway through the second half after a strong drive by the St Mary's forwards.
Buccaneers' lights went up after another great run by Martin Cahill earned them a penalty try, but McPhilips put his side back into a deserved lead.
Conboy converted and added the final touch with a try and conversion.
SCORING SEQUENCE: 5 mins: T Robinson try, C Glynn con, 0-7; 20: C Glynn pen, 0-10; 22: C Glynn drop goal, 0-13; 34: A Conboy pen, 3-13; 43: D Clare try, Conboy con, 10-13; 54: Conboy pen, 13-13; 61: K Jennings try, 18-13; 62: penalty try, Glynn con, 18-20; 80: C McPhilips try, Conboy con, 25-20; 82: Conboy try, con, 32-20.
ST MARY'S: P McKenna, J Norton, K Lewis, G Gannon (Capt), J McWeeney, A Conboy, C McPhilips, P Tucker, G Hickie, D Clare, E Keane, J Ryan, M Browne, S Jennings, K Jennings.
BUCCANEERS: O Grennan, T Robinson, W Wallace, J Meagher, M Devine, C Glynn, C Keane, J Screene, J McVeigh, M Cahill, G Schuman, N Smullen, E Brennan (Capt), F Lyons, A Hanley.
Referee: S McDowell (Ulster Branch).