Both sides' recent poor form was evident in the opening exchanges as they proceeded with trepidation which led to a lack of chances.
It was Brighton who eventually threatened one of the goalkeepers, though, when the tricky Will Buckley created an opening for Andrew Crofts, only for the ex-Norwich midfielder to fire over.
The prolific Craig Mackail-Smith ended a four-game spell without a goal when he found the net twice in a draw with Leeds last Friday, but he was unable to make the most of the opportunities which fell his way here.
First, the Scottish international, who would have had a hat-trick against the Whites had he not missed a penalty, headed tamely at Robert Olejnik.
Mackail-Smith then met another flighted cross with his head but could only flick the ball wide as a forgettable first 45 minutes drew to a close.
Gus Poyet's half-time words clearly had their desired effect on the Seagulls as they upped the ante after the interval.
Ashley Barnes' driven shot from distance forced Olejnik to push the ball around a post as the home crowd stirred into life.
Buckley looked the most likely to make something happen and Olejnik was tested once more as the winger's venomous effort swerved in front of him, with Buckley heading the subsequent rebound well wide.
Poyet's side came closer still just before the hour mark as Andrea Orlandi let the ball run across his body before firing a left-footed effort against a post.
Substitute Dobbie had a goalbound-effort blocked before Poyet handed Will Hoskins his first league appearance of the season in place of the ineffective Mackail-Smith.
And the replacements paid dividends right at the end as Barnes slipped the ball through for Dobbie, who kept his composure to fire home and end the Seagull's long wait for a league victory.