Chelsea's 4-2 win over Southampton on Tuesday meant Spurs had to win to close the gap at the top back to four points, and the players were visibly nervous in the opening exchanges at Selhurst Park.
Palace had already earned wins over Chelsea, Arsenal and Liverpool and were good value on Wednesday until Christian Eriksen's beat Wayne Hennessey from 30 yards to secure a vital win.
"It was unbelievable, a very good performance," Pochettino told Sky Sports. "I think second half we played much better than in the first half.
"It was difficult in the first half for us to move the ball and find the space but we changed the shape at half-time and it was more fluid, we started top find the space and started to push Palace deeper and deeper.
"It was good to get the three points and be alive in the race for the title. The challenge is to keep going.
"I am very pleased for Christian Eriksen. I need to see the goal on television but from my position it was a great goal."
Next up for Tottenham is the north London derby againt Arsenal, likely the last ever at White Hart Lane ahead of an expected temporary move to Wembley Stadium.
Spurs have now won eight on the bounce in the Premier League to all but confirm they will finish above their rivals, but Pochettino was not understating the importance of Sunday's clash.
He continued: "It is always better to win but it is true [the Arsenal game] is a big derby, perhaps the last at White Hart Lane and I think it will be an exciting game.