Tottenham manager Antonio Conte says "nobody could have imagined" his team would still be in the race for Champions League qualification when he arrived in November.
Son Heung-min scored twice and Harry Kane rediscovered his touch in front of goal as Spurs beat Leicester to boost their hopes of a top-four Premier League finish.
Tottenham moved briefly into fourth place with the win, but neighbours Arsenal regained the spot by beating West Ham later on Sunday.
"It was vital to get three points. There was a lot of pressure but I told my players to enjoy this moment because we deserved it after really great work that we did in these six months," said Conte, who joined Spurs after they sacked Nuno Espirito Santo.
"No-one could have imagined when I arrived in November we could be in this race still, but these players are deserving to fight for such an important place. It is not easy to qualify for the Champions League in England."
England captain Kane, goalless in his previous five Spurs games, headed in the opener from Son's corner.
Son stroked in the second after being picked out by Dejan Kulusevski, then curled in a sensational third for his 19th league goal of the season.
Leicester's Kelechi Iheanacho scored a consolation with a crisp strike.
"It was a great, great afternoon, a great match and a great performance from the team. We totally deserved it," said Son, who trails Liverpool's Mohamed Salah by three goals in the race to finish as the Premier League's top scorer this season.
"Winning the Golden Boot is not important for me. Scoring goals is really good but you can't score alone. You need the team.
"If I get the chances, then I will try to score. We want to finish in the Champions League and I want to play in the Champions League."
Leicester manager Brendan Rodgers made eight changes to his starting XI, with the game coming in the middle of their two-legged Europa Conference League semi-final against Roma.
The Foxes remain 11th in the Premier League table, meaning winning Europe's third club competition seems their only realistic route into continental action next season.
With upcoming matches against title-chasing Liverpool and top-four rivals Arsenal, Tottenham knew the importance of returning to winning ways against a Leicester side with more pressing priorities this week.
Spurs had not won either their two previous matches, punished for a sluggish display in a home defeat by Brighton and unable to break down a stubborn Brentford last weekend.
What was most startling about those performances, considering the amount of attacking talent at their disposal, was Spurs' inability to record a shot on target in either game.
But Conte's side led at half-time at Tottenham Hotspur Stadium with their only effort on target, then rediscovered their attacking verve after the break.
Their trusted combination up front delivered for the first when Son clipped a corner towards the near post, where Kane had escaped his marker Daniel Amartey to power in.
"We scored early in the first half and that changed the game - we knew we'd have more space in the second half," said Son.
The start of the second half was also tight before Son - helped by the running and guile of Kulusevski, introduced as a substitute after surprisingly being left on the bench - ensured there was no way back for Leicester.
Tottenham's reinvigoration in front of goal particularly pleased Conte, who took over from former Wolves boss Nuno with Spurs eighth in the table.
"I think we were more clinical in this game. There was space for us and we exploited it very well. That was the key," said the ex-Chelsea, Juventus and Italy manager.
