Son has struggled badly this season and his poor form convinced Tottenham's absentee boss Antonio Conte to axe him for the Premier League clash.
Prior to this weekend, the 30-year-old had scored in only four matches this season.
But Son made his point to Conte as he came off the bench to net Tottenham's second goal after Emerson Royal put the hosts ahead in the second half.
Son's ninth goal in all competitions this season mirrored his hat-trick against Leicester in September, which came after he was dropped and then introduced as a substitute.
Tottenham's win over their struggling London rivals lifted them one point above Newcastle into fourth place, although the Magpies have a game in hand.
Conte was watching on television back home in Italy after deciding he had returned too soon following his gallbladder surgery, with assistant coach Cristian Stellini taking instructions from his recuperating manager.
It was a much-needed victory for Tottenham, who were thrashed at Leicester last weekend, then lost 1-0 at AC Milan in the Champions league last 16 first leg.
Stellini has now won all three matches while deputising for Conte this season.
West Ham remain third bottom after a first defeat in four league games.
Just 46 seconds had gone when West Ham went close through Jarrod Bowen, who hit a half-volley just wide.
Tottenham were angered when a VAR check ruled that Richarlison's shot, which clearly struck Thilo Kehrer's out-stretched hand, was not worthy of a penalty.
Tottenham struggled to find any rhythm as the half wore on and their first shot on target from Pierre-Emile Hojbjerg drew sarcastic cheers from frustrated fans.
Richarlison has struggled to make an impact since his £60 million ($72 million) move to Tottenham from Everton last year, scoring just two goals.
The Brazilian's lack of form was evident again when he took a poor angle from Harry Kane's pass, losing his position and allowing Lukasz Fabianski to save.
Richarlison shot straight at Fabianski again early in the second half, but Tottenham finally made their territorial dominance count in the 56th minute.
Ben Davies's pass split the West Ham defence and Emerson showed unexpected composure for a player with just one goal this season as the right-back drilled a confident finish past Fabianski from just inside the area.
Fraser Forster preserved Tottenham's lead moments later with a fine save from Bowen's powerful drive.
Son's exile ended when he came on for Richarlison in the 67th minute and he was on the scoresheet within five minutes.
Kane's superb pass took two West Ham defenders out of the game and Son's touch was perfect as he controlled deftly before slotting past Fabianski from 12 yards.
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