Crystal Palace slumped to 20th place in the Premier League table after suffering defeat at White Hart Lane, with Christian Eriksen and Jermain Defoe getting the goals.
Palace had completely dominated the first half and Jason Puncheon missed a penalty, but they were second-best after the break and were left ruing their earlier wastefulness.
Crystal Palace were dominant in the early stages, and soon had a clear chance to score as Marouane Chamakh, who had burst down the left channel, was clumsily brought down in the box by Moussa Dembele, the Belgian getting nowhere near the ball. Jason Puncheon stepped up to take it... but his staggered run led to one of the worst spot-kicks for quite some time in the Premier League, blazing the ball high and wide by quite a distance.
Yet Palace kept coming, and Spurs struggled to get into the game at all. A pair of long-distance efforts from Nabil Bentaleb were the only shots the hosts could muster, the first tame and low, but the second beating Julian Speroni and cannoning off the inside of the post, along the goal-line and out in a heart-stopping moment for the travelling supporters.
Yet it was Palace who were by far the better side, with Puncheon and Chamakh causing havoc on the counter-attack. The latter almost teed up the former in one perfect sweeping move, but he slightly overcooked his pass and allowed the ever-alert Hugo Lloris to collect.
As was perhaps slightly predictable, Palace were made to pay for their earlier profligacy with a sucker-punch early in the second half. Emmanuel Adebayor used his height to flick on a long ball and find Christian Eriksen, who provided a smart and powerful finish to put Spurs into the lead and erase their first-half troubles.
Jermain Defoe was then introduced for the hosts to begin his farewell tour at White Hart Lane (until inevitably returning on loan in a desperate bid to get in England's Euro 2016 squad, obviously) and had a decent chance after getting into the left channel but flashed his shot across Speroni and the face of goal.
Defoe was to get another chance, however, and made no mistake at the second time of asking, running onto a ball from Aaron Lennon and lashing home with a trademark finish to seal the win for Tottenham. It was a pretty rough start for Tim Sherwood's side, but they got there in the end. Palace's errors will prove costly, however, as the defeat left them bottom of the Premier League.
Tottenham Hotspur: Lloris, Walker, Dawson, Chiriches, Rose, Lennon, Bentaleb, Dembele, Eriksen, Adebayor, Soldado.
Goals: Eriksen 50', Defoe 72'
Crystal Palace: Speroni, Mariappa, Gabbidon, Delaney, Parr, Bolasie, Ward, Jedinak, Puncheon, Jerome, Chamakh.