Having dragged themselves away from danger with back-to-back wins over Coventry City and Chelsea, Roberto De Zerbi’s side looked determined to continue their momentum against a misfiring Palace.
The hosts were given a helping hand just 13 minutes into the contest, as Jean-Philippe Mateta was shown a straight red card for a studs-up challenge on Micky van de Ven's Achilles, following a VAR review.
Armed with the man advantage, Tottenham broke the deadlock soon after, when a deep corner from Mohammed Kudus picked out Gray, who guided a superb header back across Dean Henderson and into the far corner.
De Zerbi’s men went in pursuit of a second goal before half-time, but Dominic Solanke glanced a header over the bar, before Andy Robertson’s speculative effort from range was comfortably saved by Henderson.
Tottenham’s relentless pressure continued at the start of the second period, as Solanke saw a sharp strike pushed away by Henderson, while at the other end, Dwight McNeil had a promising effort blocked in a rare foray forward for the visitors.
After further opportunities for Pedro Porro and Mathys Tel, a second goal finally arrived for the hosts with 17 minutes remaining when Van Hecke nodded a close-range rebound over the line after his initial header was tipped onto the bar by Henderson.
Kudus spurned a glorious chance to add further gloss to the scoreline, while Henderson stood firm to deny substitute Dejan Kulusevski late on, as Spurs cruised to a convincing three points to move up to eighth in the table.
As for Palace, pressure continues to mount on Pierre Sage, with the Eagles falling to their sixth defeat in nine league matches.
Flashscore Man of the Match: Jan Paul van Hecke (Tottenham Hotspur)