Brighton looked to have snatched a creditable draw at White Hart Lane, until the Republic of Ireland international produced a fantastic piece of skill inside the last few minutes to knock them out of the competition.
Saegulls striker Leon Knight could have broken the deadlock after just seven minutes when his low shot from the edge of the box produced a fine save from Paul Robinson diving low down to his right.
Mark McGhee's side continued to put pressure on the Spurs goal and almost took a shock lead after just 15 minutes when Richard Carpenter's superb 25-yard drive came back off the crossbar.
The ball rebounded to defender Kerry Mayo who fired the ball high over Robinson's goal.
Tottenham forced their way back into the game and Keane caused all kinds of problems for the Brighton defence on 20 minutes when he weaved his way into the area and struck his shot just over the bar.
Keane came even closer to opening the scoring for the home side on 31 minutes.
Erik Edman's high ball into the box was flicked on by Stephen Kelly into the path of Keane whose close-range shot also came back off the crossbar.
But Tottenham finally made their Premiership status count when they opened the scoring on 38 minutes.
Michael Brown played a short corner into the path of Reto Ziegler whose cross fell perfectly for Ledley King.
The Tottenham skipper's looping header flew over Brighton keeper Michel Kuipers into the corner of the net.
But Knight almost grabbed an equaliser for Brighton on the stroke of half-time when his header inside the box forced Robinson to tip the ball over the bar.
Brighton refused to lie down and gave their 5,000 away support something to cheer about on 48 minutes when they snatched an equaliser.
Carpenter planted a sweet free-kick from the edge of the box past the stranded Robinson into the corner of the net.
In an open encounter, Tottenham almost regained the lead straight away on 55 minutes when Jermain Defoe fired a blistering shot from the edge of the box, which produced an excellent save from Kuipers.
But Brighton were also looking to secure a fourth round place and almost took the lead themselves on 64 minutes.
Mayo's free-kick was flicked on by Gary Hart and Robinson showed why he is England's number one by superbly turning the ball around the post.
But for all the hard work Brighton put into the game, it was a piece of magic by Keane on 82 minutes that ended their hopes of reaching the next round of the competition.
Edman's ball into the box found Keane who produced a fantastic turn and fired the ball into the corner of the net past the stranded Kuipers.
Man of the Match: Robbie Keane - The Irishman proved to be the matchwinner for Spurs as he showed his class with a superb clinching goal late on.