Spurs have made a habit of recovering from slow starts to win in recent months, but this time they failed to capitalise on scoring after just five minutes.
Brennan Johnson was left with the simple task of tapping into an empty net from Timo Werner's cross.
West Ham were under pressure to respond after collapsing from 3-1 up to lose 4-3 at Newcastle on Saturday.
The Hammers were quickly level as Jarrod Bowen's corner flew in off the back of Kurt Zouma.
A draw kept West Ham one point ahead of Newcastle in seventh, but they missed the best chance to take all three points when Michail Antonio fired straight at Guglielmo Vicario.
Tottenham close to within two points of Aston Villa in fourth and extend their lead over sixth-placed Manchester United to nine points.
Everton's unwanted record
Injury-hit Newcastle's hopes of European football next season were dented by Dominic Calvert-Lewin's late equaliser for Everton from the penalty spot.
Alexander Isak scored for the fifth consecutive game at St James' Park to open the scoring.
The Swede took his tally for the season to 19 as he cut inside Jarrad Branthwaite and slotted into the far corner on 15 minutes.
How Sean Dyche longs for a striker of Isak's quality. But Calvert-Lewin ended a near six-month goal drought from the spot after Ashley Young was hauled down inside the box by Paul Dummett.
Everton set a new club record winless run of 13 Premier League games to leave their 70-year stay in the top flight still at risk.
The Toffees edge four points above the relegation zone but have the threat of a second points deduction for breaches of financial rules hanging over them.
Nottingham Forest pulled three points clear of the relegation zone with a first-half blitz of Fulham to win 3-1.
The home side sped out of the blocks at the City Ground as Callum Hudson-Odoi and Chris Wood smashed home inside the first 19 minutes.
Fulham boss Marco Silva showed his disgust by making a triple substitution after just half an hour.
However, even that did not halt Forest's momentum as Morgan Gibbs-White made it 3-0 in first-half stoppage time.
Fulham pulled one back through Tosin Adarabioyo in the second half but it was too little, too late for the Cottagers.
Second-bottom Burnley are now unbeaten in four but slip six points adrift of safety after a 1-1 draw at home to Wolves.
Jacob Bruun Larsen put the Clarets in front, but Rayan Ait-Nouri's header secured Wolves a point.
Bournemouth climbed above Chelsea into 11th thanks to Justin Kluivert's winner as they beat Crystal Palace 1-0.
