Harry Kane opened the scoring with his second goal in as many games, before Lucas Moura doubled their lead with a powerful header from close range
Palace, who had asked the Premier League to postpone the game because of a Covid-19 outbreak, which included a positive test for manager Patrick Vieira, never got going in north London.
With Vieira self-isolating, assistant manager Osian Roberts took charge of the team, which had to play for nearly an hour with 10 men.
Their talisman Wilfried Zaha felt aggrieved about his sending off for two bookable offences in the first half, before Son Heung-min sealed the win with a third for Tottenham after the break.
Spurs are unbeaten in six league games under Antonio Conte and are six points behind fourth-place Arsenal with three games in hand, while Palace are 12th in the table.
Spurs focus on the task as Palace struggle
While most of the country was tucking into their second round of Christmas lunch, rumours were starting to emerge that the game would be postponed.
Vieira had confirmed on Friday that there had been “a couple of cases” at the club, and the situation had reportedly got worse, but it was decided on Sunday that the game would take place.
Despite the outbreak, the visitors only made one change to the side that drew with Southampton in their last league game on 15 December as centre-back Joachim Andersen replaced Marc Guehi, who was available from the bench.
Both sides started slowly, but once the Christmas indulgence had been digested, it was Spurs who took the initiative.
Kane and Boxing Day goals go hand-in-hand and the England striker extended his Premier League record to six goals in his six top-flight appearances on 26 December.
Only both goalkeepers had touched the ball fewer times than Kane before he swept Moura’s square into Jack Butland’s net.
Two minutes later, Moura showed plenty of determination to climb above Andersen and nod in the second.
Zaha had been penalised for a clip on Davinson Sanchez before a needless push on the Spurs centre-back made his side’s task even harder.
Man of the match Moura, who could have scored another when he glanced a header wide inside the six-yard box, did add another assist with a delicious cross for Son to side-foot his eighth league goal of the season.
Palace failed to register a shot on target, but the one bright spot was the performance of full-back Tyrick Mitchell.
He gained possession more times and played more passes in the opposition half than any of his team-mates.