The Hammers ended a run of four successive defeats with a comfortable success over their capital rivals at Upton Park.
The game turned midway through the first half when Younes Kaboul was given a straight red card for bringing down Stewart Downing when he was through on goal.
The resulting free-kick on the edge of the box from Andy Carroll was brilliantly tipped over by Hugo Lloris, but the England striker was on hand to head home the resulting corner, albeit with a little help via Harry Kane's inadvertent flick-on.
The second arrived on the stroke of half-time and this time Downing was the scorer as he claimed his first goal in West Ham colours as he curled a free-kick through the Tottenham wall and past Lloris.
Had it not been for Lloris the scoreline could and should have been greater as he produced wonderful stops from Matt Taylor and Mohamed Diame.
Tim Sherwood's side began well enough, with Kane close to an opening goal after 52 seconds when Adrian's rushed clearance ricocheted off him and spun wide.
Emmanuel Adebayor was unable to cap a wonderful, flowing team move by striking tamely at Adrian soon after, before Carroll saw appeals for handball against Kane fall on deaf ears.
Michael Dawson appeared to then handle from the resulting corner, from which the ball broke to Guy Demel and his looping strike came off the bar.
Adrian saved a Paulinho header on goal and Downing blazed over as play swung from end-to-end, until the dimensions changed in West Ham's favour in the 25th minute.
A wicked deflection saw the ball looped over Spurs backline into the path of Downing, who, having left Danny Rose in his wake, continued on goal until being bundled over by Kaboul.
Referee Phil Dowd deemed him to be the last man and showed a straight red card, with Lloris having to be at his best to stop Carroll firing home the free-kick.
The ball went out for a corner and when Mark Noble swung it across, West Ham ended their 257-minute wait for a goal, with Carroll's header going in via a deflection off Kane.
It was a horrible moment for the 20-year-old forward, who was replaced moments later by defender Vlad Chiriches in a bid to stem West Ham's increasing momentum.
George McCartney came close to netting at the backpost before Rose almost put into his own goal, with Lloris then doing exceptionally to turn Matt Taylor's goalbound strike around the post.
The France goalkeeper could only do so much, though, and his team-mates let him down as West Ham doubled their advantage a minute before the break.
Downing hit a reasonable free-kick that would have hit the wall had Adebayor and Paulinho not parted, allowing the ball to sneak through past the Spurs goalkeeper.
It was a shocking goal which was almost added to by a Carroll volley in first-half stoppage time.
West Ham continued strongly after the restart as Mo Diame's overhead kick produced an exquisite save from Lloris, who did well to stop Kevin Nolan scoring the follow-up before Taylor curled just wide.
The Spurs goalkeeper's one-man stand continued as Carroll flicked the ball on to Nolan, with the onrushing goalkeeper spreading himself to block behind.
Adrian fumbled a Christian Eriksen cross in a rare threatening moment for Lloris' counterpart, with Sherwood bringing on Sandro and Roberto Soldado in a bid to change the dynamics of the match.
The latter quickly had an impact, receiving a booking after kicking Diame and manhandling Nolan before striking across the face of goal.
Sandro was also at the heart of things in the closing stages, blocking a shot, picking up a booking and then seeing appeals for a handball against Taylor ignored.
Adrian did wonderfully to tip over a late Rose strike, which saw West Ham end a 10-match wait for a clean sheet.