Son became the first Spurs player to score at the ground with a shot that took a deflection off Luka Milivojevic on 55 minutes.
Eriksen confirmed the win 10 minutes from time when he drove a loose ball into the net after a driving run from Harry Kane.
Palace rallied late on and Hugo Lloris saved from Patrick van Aanholt and Wilfried Zaha before Christian Benteke headed wide from close range.
A first win in six returns Spurs to third on 64 points, one ahead of Arsenal, while Palace stay 13th on 36 points.
Spurs: 13 Apr v Huddersfield (H)
Crystal Palace: 6 Apr v Newcastle (A)