It was the 25-year-old goalkeeper's debut for Spurs, having joined the North London outfit in the summer transfer window after leaving Premier League rivals Southampton.
Injuries to Dele Alli, Toby Alderweireld, and captain/goalkeeper Hugo Lloris assured that confidence, and Palace delivered on the threat.
Spurs weren't anywhere near their best in the game at Wembley after their Champions League exertions over Real Madrid during the week, but with two shots on target, they grabbed all three points with Son's goal.
Gazzaniga was arguably the best player on the pitch, and Spurs manager Pochettino has spoken highly of him, summing up his performance in one word - "fantastic".
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"No point in beating Real Madrid on Wednesday if you can't win at home at the weekend", Tottenham defender Eric Dier said.
The main talking point in a quiet first half came when Harry Kane picked up a knock following a challenge from Timothy Fosu-Mensah.
Gazzaniga also had to be alert to deny Luka Milivojevic's close-range header and Palace were made to pay for their profligacy.
That miss would prove costly for the visitors, as Son scored the only goal of the game soon after - curling the ball past Julian Speroni.
Son could have made the game safe in the final 10 minutes but dragged his shot wide when well-placed but it mattered little. We had possession, but not many chances.
"At the other end I thought we had quite a few moments of our own so it's a bitter blow to lose the game 1-0".