West Ham then doubled their advantage on the stroke of half time when Downing's free kick found its way past Hugo Lloris.
Here, Sports Mole takes a closer look at the action between the London rivals at Upton Park.
On target: 8
On target: 3
Was the result fair?
West Ham were the superior team throughout the contest at Upton Park, and that includes before Spurs went down to 10 men. The hosts looked full of adventure and intensity on what could have been a nervy afternoon, while the visitors put in a toothless display that is sure to anger Tim Sherwood.
West Ham's performance
Sam Allardyce's side saved one of their best performances of the season for when they needed it most. The Hammers did not have to do much from a defensive perspective, but it was in midfield and attack where they really excelled. There was not a single player in a claret and blue shirt who did not commit themselves fully to the cause. While there was plenty of chasing around for the ball, the team looked even more dynamic when they were in possession and bombing forward. Their physicality proved too much for Spurs in the end, and they were rewarded with three deserved points.
Spurs have been guilty of some awful displays this season, and this will rank as one of their worst. A complete lack of shape and organisation did not help their cause, while the back four completely failed to deal with the power of West Ham in the final third. Christian Eriksen looked like the only player who was capable of causing any damage to West Ham, though even he was well below par. Meanwhile, the visitors were consistently impotent in attack. It tells you something that Hugo Lloris was Tottenham's star man as a string of fine saves kept the score down.
Sports Mole's man of the match
Mark Noble: The West Ham midfielder was full of energy, acting as a driving force for his side from the centre of the pitch. The Hammers favourite also did a great job of stifling Spurs' creative players throughout.
There is sure to be an inquest in relation to West Ham's second goal as the Tottenham wall provided no protection for Lloris from Downing's free kick. Emmanuel Adebayor and Paulinho in particular were at major fault as they failed to stand strong.
Phil Dowd made a big decision when he chose to send off Kaboul for a foul on Downing. It could be argued that the Spurs defender was not the last man, though it is likely that the official made the right decision in the end. However, he could easily have sent off Roberto Soldado for putting his hands around the throat of Kevin Nolan. Instead, Dowd opted to show the Spaniard a yellow card.
West Ham: The Hammers end their season next Sunday when they travel to title challengers Manchester City.
Tottenham: Spurs see their campaign finish at home next Sunday as Aston Villa make the trip to White Hart Lane.