Roberto Soldado ended his personal goal drought and kept Tottenham Hotspur's fast-fading hopes of a top-four place alive with the only goal in a 1-0 victory over relegation-threatened Cardiff City at White Hart Lane.
Sunday's win helped consolidate Tottenham's hold on fifth place, although they remain four points adrift of Manchester City, who lie fourth, having played two games fewer than Spurs.
"It's a huge ask (qualifying for the Champions League) but one we have to believe in," Spurs manager Tim Sherwood told Sky Sports.
"It is more difficult than ever because there is so much competition at the top of the table, but we are looking upwards rather than behind us."
For Cardiff, a seventh successive away league defeat leaves Ole Gunnar Solksjaer's side second bottom, three points off safety, and capped a week in which Malaysian owner Vincent Tan again reiterated his threats to sell the club if supporters continued to object to his regime.
Soldado had been under growing pressure after failing to score in eight previous games, amid reports his spell at Tottenham could end after just one season.
But the striker justified the faith shown in him by Sherwood - whose own future has been thrown into doubt after Dutch national coach Louis van Gaal was linked with a move to White Hart Lane - with the decisive first-half goal that built on the midweek Europa League victory over Dnipro.
That European win had lifted spirits following the disappointing defeat at Norwich that dealt a severe blow to the north London club's hopes of securing a place in next season's Champions League.
Andros Townsend started the move in the lead-up to Soldado's goal, collecting Hugo Lloris' clearance and running powerfully up the centre of the pitch before finding Adebayor on the left hand of the Cardiff area.
The Togo striker held the ball up then squared for Soldado, who had been allowed to find space 10 yards out despite the presence of three Cardiff defenders, and the Spaniard took one touch before volleying past David Marshall.
The reaction of the Tottenham players as they mobbed their teammate spoke volumes about the build-up of tension during Soldado's goal-drought.
"We have been wishing it in for him," said Spurs captain Michael Dawson. "He's settled in well and we are just delighted to see him score."
