Matheus Nunes's last-gasp strike sparked wild celebrations from Pep Guardiola and his players as they climbed to third place in the Premier League.
Paris Saint-Germain survived a second half onslaught to beat Aston Villa 5-4 on aggregate and reach the Champions League semi-finals despite a 3-2 defeat on Tuesday.
Arne Slot's side lost their 26-match unbeaten league run in an error-strewn 3-2 loss at Fulham.
Aston Villa took the lead in the first half in Paris through Morgan Rogers only for the hosts to turn the game on its head.
Khvicha Kvaratskhelia scored one of the great Champions League goals as Paris Saint-Germain came from behind to beat Aston Villa 3-1 in the first leg of their quarter-final tie.
Aston Villa manager Unai Emery is relishing the prospect of taking on Paris Saint-Germain in the quarter-finals of the Champions League
Marcus Rashford returns to Paris Saint-Germain with Aston Villa on Wednesday seeking a hat-trick of wins at the home of the French champions
Aston Villa sit below fifth-placed Manchester City only on goal difference and moved to within one point of Chelsea in fourth.
Marcus Rashford's first goals for Aston Villa inspired a 3-0 win against Preston that sent his side into the FA Cup semi-finals for the first time in 10 years.
Ian Maatsen scored in between Marco Asensio's brace as Unai Emery's side romped to a 6-1 aggregate victory.
Just six points separate faltering Nottingham Forest in third place from Aston Villa in 10th, with a top-five finish almost certain to secure a place in Europe's top club competition next season.
Chelsea duly delivered with three first-half goals through Christopher Nkunku, Pedro Neto and Levi Colwill for just a third league win 11 games.
Liverpool's Premier League title charge was slowed by Aston Villa after a pulsating 2-2 draw on Wednesday left neither side satisfied.
Liverpool suffered a stunning FA Cup exit on Sunday in a 1-0 defeat to Championship strugglers Plymouth
Ruud van Nistelrooy returns to Manchester United with his struggling Leicester this weekend, aiming to inflict more pain on his former club in the FA Cup
Aston Villa signed Marcus Rashford on loan from Manchester United for the rest of the season on Sunday to end the England international's exile under Ruben Amorim at Old Trafford
Aston Villa have one last chance to seal automatic qualification for the Champions League last 16 when they face Celtic in a crucial 'Battle of Britain' clash on Wednesday
Aston Villa boss Unai Emery is ready to make a move for Villarreal defender Juan Foyth as he searches for a new centre-back