Replacements: David Byrne, John Leahy, David O'Mahony, Killian O'Keeffe, Andrew O'Leary.
Replacements: Cillian O'Neill, Adam Howard, Leo Auva'a, Shaun Berne, Fergal Lawlor.
But Dolphin, who have slipped to seventh in the table, recovered well in the second quarter with unconverted scores from Darren Sweetnam and American international back rower John Quill.
The Dubliners dominated the opening stages of the game, although out-half Crosbie was unable to convert his first shot at the posts.
He was on target when adding the extras to his own try though, which came from a well-executed rolling maul.
Ireland Under-20 hopeful Robb, who combined with John Kennedy in the centre, then crashed through for 'Belvo's second try, moving them 12-0 ahead by the midpoint of the first half.
Dolphin improved in the second quarter and displayed their own attacking qualities, as they released right winger Sweetnam for an unconverted try out wide.
That score seemed to settle the Cork club down and they exerted further pressure before Quill touched down just before the break - Sweetnam, Darren O'Shea and centres Cian Bohane and Eric Moloney were all involved in the build-up.
There was still time for Quill to see yellow on the stroke of half-time, but Crosbie missed the resulting penalty to leave 'Belvo 12-10 ahead at the turnaround.
There was little between the sides at a crucial juncture early in the second half as Crosbie suffered another penalty miss and Dolphin were held up close to the Belvedere whitewash.
The game's turning point came when Dolphin veteran Barry Keeshan's drop goal attempt was blocked by Jack Conan and the 'Belvo number 8 hacked the ball ahead twice before gathering it for a superb solo try that Crosbie converted.
With Leinster's Leo Auva'a adding his bulk to the 'Belvo pack, the Dubliners saw out a deserved away win with fellow replacement Shaun Berne slotting a final penalty late on.
'Belvo left the Cork ground with silverware in the form of the McCarthy/O'Reilly Cup, which was crafted in honour of former Ireland internationals Jim McCarthy and Tony O'Reilly.
Referee: Mark Connolly (IRFU)