"Last night I saw Michel wasn't very good so I prepared already and Toni (Jimenez), the goalkeeper coach, told me I was going to play today so I was ready from last night".
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.
"It was a tough game for us after Wednesday".
There was little sign of the highlights to come when Gazzaniga was perhaps lucky not to be penalised in the third minute as he cuffed Mamadou Sakho around the head, rather than play the ball, under a teasing Zaha cross.
And despite some good chances falling for Palace, and in particular for Wilfried Zaha, Son's strike was enough to give Spurs all three points at Wembley.
Palace stuck gamely to its task, repelling numerous crosses and limiting Spurs to long-range efforts, and home frustrations soon turned to fears when Harry Kane went down clutching his ankle after taking a kick from Tim Fosu-Mensah.
Palace looked the more likely to break the deadlock at the start of the second half and should have taken the lead.
Palace continued to knock at the door, Gazzaniga again forced to save by Luka Milivojevic after the hosts failed to clear a corner.
The goal came after 64 minutes when the ball fell to Son Heung-Min on the edge of the box after a cross was not properly dealt with and the South Korea global curled an outstanding finish past Speroni and into the corner.
Palace boss Roy Hodgson, whose side remain bottom, said: "I thought we worked hard and there weren't that many shots to worry about".