The midfielder's decisive strike earned a 2-1 win over last season's beaten play-off semi-finalists, sending the majority of a sold-out Elland Road into delirium on a day which had been heralded as the first of a new era at the club.
Leeds had not appeared so sure-footed early on, however, and it was Brighton who made the first impression as Andrea Orlandi forced Kenny into action from 25 yards.
The early stages certainly gave a nod to Garcia's philosophy - Brighton were happy to roll the ball around - and with 13 minutes gone it bore fruit as Ulloa haunted Leeds again.
Brighton had been largely contained since their goal at that point, but suddenly reintroduced themselves to the game at the three-quarter mark with only Kenny stopping them from regaining the lead.
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A late goal at Elland Road saw 10-man Brighton beat nine-man Leeds to secure a play-off place for Gus Poyet's side in an ill-tempered match.
Will Buckley opened the scoring for Brighton in the 10th minute, with Leeds midfielder Rodolph Austin shown red shortly after.
Brighton's Inigo Calderon was sent off midway through the second half for a challenge on El-Hadji Diouf, who scored the resulting penalty before being sent off himself after appearing to abuse the away fans following the goal.
Jose Ulloa had the final word as he headed a late winner for Brighton.