Alex Dunlop and Adam Hughes scored two tries apiece as Terenure College got the better of Galwegians at Crowley Park.
The Dubliners struck for tries after nine and 24 minutes to lead 10-6 at the break.
Two Nick Wakley penalties kept the hosts in contention, although they did lose Connacht flanker Matt Lacey to a yellow card.
'Nure prop Stephen Nolan also spent time in the sin bin and the Dubliners had to cope with losing player-coach James Blaney through injury.
'Wegians saw Anthony Barrett cross the whitewash but they had Lacey sent-off for earning his second yellow late on.