Defoe’s mis-hit opener in the 37th minute was cancelled out by Luciano Becchio’s equaliser at the end of the first half, but the England striker poached a second-half winner and then a late third to book the Londoners a fifth-round tie at Bolton on the weekend after next.
Defoe admitted he was relieved to have overcome the challenge.
“That was a difficult game. A cup tie is always difficult,’’ he said. “Away from home it was a great performance from the lads, I am pleased with the win.’’
Leeds had put themselves back on the national stage with their third-round upset at Manchester United and won more new friends with an inspired late fightback 11 days ago in the initial tie at White Hart Lane.
But ultimately Simon Grayson’s League One upstarts ran out of legs against polished Champions League contenders, who will now have one eye at least fixed on the FA Cup.
Defoe missed a hat-ful of first-half chances to put the tie to bed, just as he had done against Leeds in London, and Grayson’s side harried and chased to keep most in an Elland Road crowd of 37,704 full of hope until the visitors’ decisive third goal.
Leeds pair Bradley Johnson and Andrew Hughes returned to the starting line-up in place of ineligible loanees Gary McSheffrey and Shane Lowry.
Tottenham recalled Sebastien Bassong for Ledley King, while Niko Kranjcar and Jermaine Jenas also returned, with Wilson Palacios and Luca Modric making way.
Defoe fluffed a golden chance to give the visitors a first-minute lead when pouncing on a blunder by Hughes, only to scuff his shot and Bassong volleyed an early corner over the crossbar.
Peter Crouch then chested down for Defoe to fire a shot inches wide as Spurs burst out of their blocks, just as they had done at White Hart Lane 11 days ago.
Defoe squandered another chance when one-on-one with Casper Ankergren in the 25th minute as the striker’s low shot came back off the Danish goalkeeper’s legs. Defoe’s searing pace then caught Leeds flat-footed again when chasing a long ball over the top, but Lubo Michalik’s desperate lunge went unpunished by referee Andre Marriner.
Ankergren thwarted Defoe again 10 minutes before the break, this time after Tom Huddlestone’s lay-off, but the pint-sized forward broke the deadlock in the 37th minute, ironically from a mis-hit effort after David Bentley had cleverly slipped his marker, Hughes, down the right.
Defoe controlled Bentley’s cross and miscued to send the ball arcing slowly over Ankergren into the top corner.
Spurs goalkeeper Heurelho Gomes then saved brilliantly to keep out Michalik’s header from Howson’s free-kick as Leeds launched an immediate response.
But there was no denying Becchio in first half stoppage-time.
Beckford’s shot on the turn was parried by Gomes, but the Argentinian forward rammed home the rebound to level the scores.
Ankergren kept out Dawson’s 59th-minute header which appeared destined for the top corner and was equal to Bentley’s fierce drive soon after as Tottenham probed – but Leeds refused to buckle.
Defoe sidefooted home Kranjcar’s cross in the 68th minute, but his effort was ruled out for offside.
The League One side were not to be spared in the 73rd minute however. This time Bentley’s low cross eluded the Leeds rearguard and Defoe nipped in to turn the ball home from six yards. Leeds never stopped running and pressed for another unlikely equaliser, but with time running out Defoe latched on to another ball over the top to round Ankergren and roll home his third in time added on.
LEEDS: Ankergren, Bromby, Naylor, Michalik, Hughes (White 76), Howson, Doyle, Johnson (Crowe 86), Snodgrass, Beckford, Becchio (Grella 86).
TOTTENHAM: Gomes, Corluka, Dawson, Bassong, Bale, Bentley, Huddlestone, Jenas, Kranjcar, Crouch, Defoe.
Referee: Andre Marriner (W Midlands).