With Hugo Lloris and Michel Vorm injured, the Argentine started against London rivals Palace and gave a good account of himself.
I was nervous for the first three seconds, and after that you get the atmosphere.
Mauricio Pochettino's side, fresh from beating European champions Real Madrid in midweek, found Palace a hard nut to crack at Wembley and could have been behind before Son curled in the victor midway through the second half.
"No point in beating Real Madrid on Wednesday if you can't win at home at the weekend", Tottenham defender Eric Dier said.
"The last seven games, we played all the games, were very emotional for the players and they're not machines, they need time to recover from every effort".
Palace have four points from 11 games but could count themselves unfortunate as Scott Dann was twice denied by Tottenham's debutant keeper Paulo Gazzaniga while Wilfried Zaha wasted a great chance shortly before Spurs scored.
Two minutes later, Spurs were again thankful to the alert Gazzaniga, who made a reflex stop from Luka Milivojevic's header - and within moments of that save they had taken the lead.
With the 64th-minute victor, Son increased his goals tally to 20 in 72 games to overtake the record of Park Ji-Sung who scored 19 league goals in 154 games.
Zaha had half a chance to level but his final effort was neither cross nor shot, and with 76 minutes gone Spurs made another switch as Kane departed the action and was replaced by Fernando Llorente.
"We knew the quality they have and that they would dominate possession especially in the latter half of the middle".
"With any luck whatsoever we would have come away with some points from the game".