In a match devoid of any cutting edge, the hosts showed why they remain the Sky Bet Championship's tamest outfit in front of goal, having found the net only six times in a dozen matches.
Glovers boss Gary Johnson made four changes to his side that were thrashed 4-1 at Middlesbrough before the international break, with Republic of Ireland international Paddy Madden, whose 23-goal haul fired Yeovil to promotion from League One last season, left out of the squad.
The injury-hit visitors, looking for their first win in four attempts and first goal on the road since August, started the game brightly with on-loan Cardiff midfielder Craig Conway impressing on the left flank.
Oscar Garcia's side cut through the static Yeovil rear-guard after only four minutes and came inches away from snatching an early lead when Will Buckley took advantage of a quick free kick to feed Ashley Barnes, who blazed over from close range.
Despite their opponents making the 160-mile trip to the South West, it was the Glovers who continued to look jaded with goalkeeper Wayne Hennessey keeping Albion out in the early exchanges with a smart save from Barnes's powerful header.
The hosts' brightest moments in an otherwise drab first half came through debutant Fraser Fyvie, who signed on loan from fellow Championship side Wigan this week.
A first curling free-kick was headed narrowly over by Shane Duffy, before the 20-year-old's second set piece stung the palms of Albion goalkeeper Tomasz Kuszczak.
But Fyvie's debut proved short-lived after he fell heavily under a bruising tackle from former Glover Rohan Ince, and left the field mid-way through the first half clutching his shoulder.
Brighton poured forward in a bid to take advantage of Yeovil's misfortune with Barnes and Buckley both spurning good opportunities to break the deadlock.
The Huish Park faithful were finally awoken from their slumber early in the second half when Sam Hoskins broke away promisingly, but his disappointing strike did little to worry Kuszczak in the Albion goal.
Yeovil's early effort in the second period saw confidence flow back into their veins, with midfield talisman Ed Upson breaking away from his marker before hitting a ferocious 25-yard drive straight at the goalkeeper.
Brighton brought new loan signing Leroy Lita off the bench on the hour mark in response, but it was Yeovil again who seized the initiative with Upson hitting an ambitious effort narrowly over the bar.
The Glovers came close to breaking the deadlock as the game began to peter out when Duffy headed an Upson corner over the crossbar.
But Brighton should have snatched all three points late on - with Buckley and Lita both spurning gilt-edged chances.