A game that looked destined to be a goalless draw sprung to life in the final 15 minutes.
Yeovil boss Russell Slade sent on substitute Andre McCollin in the 74th minute for the tiring Andy Welsh and, within three minutes, the former Fisher Athletic striker conceded the penalty that gave Brighton the lead.
He dropped back to help out his defence as they tried to defend a corner but fouled Adam Virgo and Nicky Forster drove the ball low to the left of keeper Asmir Begovic from the spot.
Yeovil had lost four consecutive matches, all away from home, and did not deserve to lose a fifth.
They were rewarded for their hard work three minutes later when midfielder Darren Way cracked home an excellent drive from outside the box.
The diminutive ex-Swansea player had been doubtful all week because of a virus but his performance typified the spirit of Yeovil's youngsters.
Before the goals Brighton had been reduced to ten men when Joe Anyinsah, making his debut on loan from Preston, was adjudged to have fouled full-back Nathan Jones in the 58th and 61st minutes and referee Paul Taylor produced two yellow cards.
The first half had seen Yeovil playing some bright attacking football especially down the wings where Welsh, making his home debut after a summer release by Blackpool, showed plenty of trickery. But no-one was able to get on the end of his crosses and Brighton defended well to keep the score-sheet blank.
In the 14th minute Yeovil's other winger, Danny Schofield, drove wide after working himself into a good shooting position and Paul Warne also got in space but failed to trouble goalkeeper Michels Kuipers.
