Barcelona, holding a 2-0 advantage from the first leg, had a penalty appeal waved away after Lionel Messi was brought down in the box early on and Neymar had a goal chalked off for offside after 18 minutes.
Messi hit the post early in the second half before City, with manager Manuel Pellegrini watching from the stands, upped the pressure and Barcelona keeper Victor Valdes pulled off a stunning save to deny substitute Edin Dzeko and defender Pablo Zabaleta fluffed a shot just wide.
Argentine Messi would not be denied a third time, however, taking advantage of Joleon Lescott's error to clip the ball home after 67 minutes and City's misery was compounded when Zabaleta was sent off for a second yellow card with 12 minutes left.
City captain Vincent Kompany scored a consolation goal on 89 minutes but Dani Alves restored Barca's lead in stoppage time.
Any thoughts that Leverkusen, trailing 4-0 after the first leg, would roll over in Paris were extinguished after six minutes when Sidney Sam nodded the visitors in front.
Marquinhos equalised with a header seven minutes later, however, before Leverkusen wasted the opportunity to retake the lead just before the half hour mark when Simon Rolfes's poor penalty was saved by Salvatore Sirigu.
Ezequiel Lavezzi steered home PSG's second early in the second half and Leverkusen's Emre Can received his marching orders for a second yellow card as the hosts cruised to a 2-1 win on the night.
Barcelona and PSG joined holders Bayern Munich and Atletico Madrid, who progressed on Tuesday, in the quarter-finals. The final four last-16 ties will be completed next week.
- Sports & Recreation
- Lionel Messi
- Pablo Zabaleta
- Victor Valdes
- Manuel Pellegrini
- Joleon Lescott