Keane's crucial goal came just moments after he had another headed effort ruled out despite the ball having been shown to have crossed the line.
The draw kept Burnley in pole position in the race towards the Premier League as they lie three points clear of Middlesbrough who beat Queen's Park Rangers 3-2 on Friday.
The late goal meant Brighton missed the opportunity of going second and they are still one point adrift of Middlesbrough.
A delighted Keane told Sky Sports: "It's justice really after the first header was ruled out. We are top of the table with seven games left -- but there is a long way to go."
The drama unfolded after Dale Stephens had put Brighton ahead in the 30th minute, only for Andre Gray to respond with his 23rd goal of the season three minutes later.
Anthony Knockaert's shot restored Albion's lead before all the drama centred on Keane.
Burnley were on the verge of losing their first league game of the year when Keane's header from a corner was ruled out despite television replays showing that it had crossed the line.
The Clarets, on course to bounce straight back into the Premier League after relegation last season, were not to be denied, however, and Keane headed home from another 93rd-minute corner from Matthew Taylor.
Hull City, who had gone five games without a win, renewed their pursuit of the top three with an impressive 4-0 rout of Bristol City to remain three points behind Brighton in fourth place.
Sheffield Wednesday are fifth on 65 points after an 83rd minute Fernando Forestieri strike earned them a 1-0 win in their Yorkshire derby at Huddersfield Town.
The battle for the final playoff spot is heating up after Cardiff City narrowed the gap on sixth-placed Derby County to just two points with Stuart O'Keefe scoring the winner in the Welsh side's 2-1 win over the Rams.
(Reporting by Ian Chadband, editing by Ed Osmond and Pritha Sarkar)
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