Cristian Stellini – standing in for absent boss Antonio Conte – left the South Korea forward on the bench following a run of poor form.
But he found the net four minutes after his introduction to add to Emerson Royal’s superb 56th-minute opener, helping Spurs into fourth spot.
Defeat for West Ham ended their three-match unbeaten run in the division and ensured they stay in the bottom three, a point adrift of safety.
Jarrod Bowen had fired wide inside 60 seconds while at the other end Oliver Skipp saw a volley deflected over.Richarlison thought he had won Spurs a penalty when Thilo Kehrer handled but referee Michael Oliver and VAR David Coote disagreed.
Hammers goalkeeper Lukasz Fabianski denied Richarlison with his feet before the break after he was set up by Harry Kane.
Richarlison and Kane both should have done better at the start of the second half before the breakthrough arrived in the 56th minute.
Pierre-Emile Hojbjerg unlocked the rigid West Ham back five with a sublime through-ball for Ben Davies, who cut inside and teed up fellow wing-back Royal to slot home from 14 yards.
Son then came on to wrap it up from Kane’s pass, slotting beyond Fabianski. Son told Sky Sports: ‘Nobody wants to sit on the bench but it’s a decision you have to accept. I tried my best to help the team. I got the chance and I was happy to score.’
West Ham boss David Moyes said: ‘There are bits of it I want to build on and hope that we take it in. The players have been challenged now, let’s see who’s up for the fight.’
MORE : Tottenham boss Antonio Conte is sidelined after operation to leave club in limbo
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