A first-half brace from Harry Kane put the visitors in charge before Christian Eriksen added a third after the interval. Two second-half goals for the Hammers from Javier Hernandez and Cheikhou Kouyate, either side of a quick-fire pair of bookings for Serge Aurier set things up for a nervy finish.
After a tense opening spell, West Ham looked to take control of the game and, were it not for some fantastic defensive work from Aurier, could have been in front when Marko Arnautovic found himself in behind the Spurs back line.
Having held firm, though, the visitors bided their time before striking twice late on in the first half.
After Eriksen was allowed space in the middle the Dane set loose Dele Alli whose cross found Kane to head home for his first goal against the Hammers away from home.
Minutes later and the same combination had Pochettino’s side two-up. Alli found space in the box and, after his effort was pushed away by Joe Hart, Kane was on hand in the middle to tap home into an empty net.
Needing something special the hosts came out for the second half on the front foot but were knocked back once again when, after holding firm following the restart, Pochettino’s side added a third.
Involved in the build-up for both first-half goals, Eriksen thought it about time he got his name on the score-sheet and, after Kane’s free-kick rattled the upright, was on hand with a fine first-time finish from just inside the Hammers’ area.
With a three goal lead having put the visitors in charge, a five minute spell opened the door for West Ham.
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Summer signing Hernandez finally bagged a home goal when he headed home from Jose Fonte’s flick on form a corner before, having picked up a yellow just before Chicharito’s goal, Aurier saw red with a silly foul on Andy Carroll earning him a second booking and an early bath.
With Spurs reduced to ten men Slaven Bilic threw on Arthur Masuaku down the left and shifted from a back five to a back four. His decision paid off when the substitute curled an inviting ball to the far post where Kouyate was more than happy to power home a header.
With a late flurry of corners for the hosts, Spurs were made to work for their three points, however, with Kieran Trippier and Harry Winks introduced to tighten things up, they held firm to pick up another three points on the road.