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.
For a full round-up of all today's action click here for in-depth match coverage from ITV Sport
More top news
Wednesday's lunch-time weather for the east
Wednesday's lunchtime weather for the west
From Faversham to Portsmouth - your photos recording the hot temperatures across the region today.