Spurs fans had started to turn on boss Thomas Frank after a run of five defeats in eight games left them 14th in the Premier League on Christmas Day.
But Sunday's victory at fellow Londoners Palace has eased some of the pressure and lifted Frank's side up to 11th — now just four points off fifth-place Chelsea.
Gray nodded home his first goal for Tottenham in the 42nd minute after a corner to the far post was headed back into the middle of the area.
Palace have now lost three league games in a row and might be struggling to deal with an increased fixture load brought about by their involvement in the UEFA Conference League.
After the win, Frank the character and resilience his team had shown.
"That is so important that we have that resilience in the team, because in a long Premier League season, you need to go to a very difficult away ground here and fight and show character," he said.
"To get a clean sheet, win 1-0, that was a massive win in many ways.
"Was it a top performance? No. Are there things we can improve? Yes. But to go here, with the season having been a little bit up and down, I think it's a huge mentality effort from the players."
Meanwhile, with each goal in his career-best scoring run, Leeds striker Dominic Calvert-Lewin is advancing his claims for a recall to the England squad ahead of the World Cup.
He netted for the sixth straight game to earn his side a 1-1 draw at Sunderland, who missed a chance to climb to fifth place.
By staying injury-free and being on the hottest streak as a professional, Calvert-Lewin is making a convincing case to be Harry Kane's back-up for England for the World Cup in the United States, Canada and Mexico.
His equaliser at the Stadium of Light came in the 47th minute and was a trademark close-range, one-touch finish, turning in a cross from Brenden Aaronson.
Calvert-Lewin now has eight goals in the league, more than any other English player.
"I am feeling good, feeling fit, strong and enjoying playing with the lads," said Calvert-Lewin.
"Lots of ups, lots of downs, you know, tests of character and I have hung in there and kept going and kept pushing back myself, and here I am now."
Simon Adingra had earlier given Sunderland the lead in the 28th minute by running onto a clever pass behind the full back by Granit Xhaka and bending a right-foot shot inside the far post.
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