Pochettino's side won 2-1 at Brighton on Wednesday to climb into sixth place in the Premier League with one game left.
Cole Palmer put them in front when he headed his 22nd league goal of the season in the 34th minute.
Christopher Nkunku's 64th-minute strike put Chelsea further ahead before Blues defender Reece James was sent off for kicking Brighton's Joao Pedro.
Danny Welbeck reduced the deficit in stoppage time, but Chelsea held on to secure a fourth consecutive league victory for the first time since October 2022.
With Newcastle losing 3-2 at Manchester United in Wednesday's other game, Chelsea moved above the Magpies.
The Blues will be guaranteed a place in next season's Europa League if they avoid defeat against Bournemouth at Stamford Bridge on Sunday, or if seventh-placed Newcastle fail to win at Brentford.
Chelsea could even finish fifth if they beat Bournemouth and Tottenham lose at Sheffield United.
It is an impressive recovery masterminded by Pochettino, who has faced criticism throughout his troubled first season in charge.
Amid calls for his sacking, Pochettino even hinted recently that he could quit at the end of the season and said it wouldn't be the end of the world if he was dismissed by chairman Todd Boehly.
But the Argentine was in more buoyant mood after Chelsea closed in on Europe, praising the club's hierarchy for sticking with their plan.
'It allows us to dream'
"We have improved results and performances. We talked about patience and when you need to build something you need time but it always looks like an excuse at a big club," he said.
"The evolution of the team is there. We have kept working and being positive and to finish in a good way would be good for the club."
Despite spending over £1 billion on new signings in their two-year reign, Boehly's consortium has left Pochettino with a young squad, whose lack of experience has often been their downfall.
But Pochettino said the win at Brighton showed they are fighting for the club.
"The Premier League is the toughest league in the world. Massive credit to the players, we fully deserved the victory. That's why I'm so happy. It allows us to dream to play in Europe next season," Pochettino said.
"The three points puts us in a very good position in the table to attack the last game against Bournemouth for the possibility to be in Europe."
