'Wegians skipper John Casserly picked up the Connacht Senior Cup from Connacht Branch Vice-President Bruce St John Blake as lock Mick Carroll scored the crucial 58th-minute try.
The 23-year-old second row touched down at the Sportsground, following a brilliant move involving John Cleary, Tom Allen and Pat Noble.
Cleary's touchline conversion made it 19-6 for the city side, and there was no way back for John McKee's Buccs.
Cleary had earlier edged the kicking duel with Buccs fly-half David Connellan. 'Wegians led 6-3 at the break, and then 9-3 thanks to talented full-back Cleary.
With 'Wegians hooker Ronan Loughney sin-binned, Connellan responded on 56 minutes to reduce that gap. Despite this and Trevor Richardson going close for the Pirates, Carroll had the final say.
In Munster, centre Ian Dowling pocketed two tries for Shannon in their 27-8 defeat of a gallant Thomond side - to help the six-times AIL champions to their first Transfield Cup title since 1995.
Tom Cregan converted Dowling's first after 4 minutes, but Division Two outfit Thomond - with Shannon scrum-half George Murphy in the sin-bin - hit back through an unconverted John Ryan try.
Cregan had kicked a 15th-minute penalty for a 10-5 half-time lead for Mick Galwey's men, and they killed off the game late on as both Dowling and Ross O'Loughlin touched down in the closing minutes.
Club Results: March 12-13
AIB League: Division Two
Highfield 20 Old Crescent 22, Woodleigh Park
Connacht Senior Cup Final:
Galwegians 19 Buccaneers 6, Sportsground
Transfield Cup Final:
Shannon 27 Thomond 8, Thomond Park