Goalkeeper Heurelho Gomes pulled off a string of superb saves as Tottenham Hotspur held Fulham to a 0-0 draw in the Premier League at Craven Cottage.
The Brazilian was at his acrobatic best to deny two second-half Bobby Zamora headers that seemed certain goals, as well as a low drive from Dempsey, who had earlier rattled the bar with a fantastic free-kick from distance.
Peter Crouch came closest to scoring for Spurs, though his volley from the edge of the area was well saved by Gomes’ opposite number Mark Schwarzer.
The result sees Fulham remain ninth, while Spurs stay in fifth position.
Tottenham went into the match on the back of two clean sheets in their wins over Manchester City and Blackburn Rovers, though a third match without conceding looked unlikely as Fulham began strongly, testing Gomes twice in the opening stages.
First Damien Duff stung the hands of Gomes with a well-struck half-volley from the edge of the area following a neat knock-down by former Spurs boy Zamora, then Gomes pulled off a superb acrobatic save from a Danny Murphy strike that was dipping under the crossbar.
Crouch thought he had given Spurs the lead with an outrageous volley on 17 minutes, but saw the effort chalked off for a foul on Niko Kranjcar in the build-up. The Croatian then struck the resultant free-kick inches wide of the near post, with Schwarzer rooted to the spot.
With Aaron Lennon well-marshalled by another former Spurs player in Paul Konchesky, it was Fulham who continued to create the better chances, and it was Clint Dempsey who came the closest to breaking the deadlock in the first half with a superb free-kick that cannoned away off the top of the bar with Gomes beaten.
Jermaine Jenas curled a left-foot effort just round the far post as Spurs started the second half purposefully, though Fulham were soon back on the front foot, with Gomes flinging himself to his left to tip away a Zamora header after the Fulham man had pulled away from Michael Dawson.
Dempsey, Duff and Zamora then combined beautifully to set up Dempsey on the edge of the area, only for the American to fire his shot too close to Gomes, before the Brazilian then pulled off a truly world-class save to keep out yet another Zamora header on 70 minutes.
With his side struggling to gain a foothold in the game, Spurs manager Harry Redknapp replaced Robbie Keane and Kranjcar with Luka Modric and Jermain Defoe, and the latter was instantly in on the action, volleying an overhead kick just over from Crouch’s knock-down.
The big striker then almost found the back of the net with 10 minutes remaining himself as he lashed a volley goalwards from 20 yards, though Schwarzer showed why he is so highly rated by Fulham fans, clawing the ball away low to his right, and getting back on his feet to block Defoe’s follow-up.
There was just time for Fulham to go close once again as Zamora fed the overlapping Duff, though after speeding in behind the Spurs defence, his strike across goal seemed the result of indecision of whether to shoot or cross, and it flashed agonisingly across goal with Dempsey a yard away from prodding home at the far post.
Michael FitzGerald / Eurosport