The 31-year-old, who will join MLS side Toronto for £6m in February, produced a typical poacher’s finish after replacing the subdued Roberto Soldado.
Christian Eriksen had earlier put Tottenham ahead just after half-time.
Palace had created chances to score, and were left to rue Jason Puncheon’s shocking first-half penalty miss.
The result continued Tottenham’s resurgence under Tim Sherwood since he replaced Andre Villas-Boas as head coach .
Spurs are yet to lose under Sherwood in the Premier League and have now collected 13 points from his five games in charge.
Tottenham head coach Tim Sherwood:
“We have a group of lads who are very talented but unless you marry that with desire you won’t get the results. If you don’t show desire your ability counts for nothing.
“Second half we picked that up. We were much better so I have to give them credit for the character they showed. We took it to the opposition after the break.
“I’ll be sorry to lose Jermain and Toronto are getting a fine goalscorer. I don’t think there are many better goalscorers than him out there.”
Crystal Palace boss Tony Pulis:
“We played so well fist half the game should have been over at half-time. The penalty miss was poor and the breaks aren’t going for us at the moment.
“I spoke to Jason Punchen at half-time about the penalty. It’s the reaction afterwards that I looked for and he did well with his performance after that.
“I think the lads have to take credit for the way they kept going. We have to take our opportunities though. Against the top teams when you are in front you have to take those opportunities.”
Written by Steve Milne
