Chelsea, who knew that two goals and a clean sheet would be enough for them to progress, had a couple of chances early on, with Frank Lampard looking for Branislav Ivanovic, while Samuel Eto'o had a shot deflected behind.
Salvatore Sirigu had to make a couple of saves in the PSG goal as Lampard continued to prove a threat from free kicks, and David Luiz tried to get the better of him with a powerful strike from long range.
The hosts were able to cut the French champions' first-leg advantage before the break, as Andre Schurrle collected a flick forward from Luiz before coolly slotting it in.
Jose Mourinho's side continued to create the majority of the chances early in the second half as Schurrle rattled the bar with a curling effort from the edge of the box just a couple of minutes after the restart.
The hosts hit the woodwork again just two minutes later when Oscar tried to find the target from a free kick, but the crossbar rescued PSG for a second time.
The visitors' first real chance of the night came just before the hour mark when Ezequiel Lavezzi won a free kick, but Petr Cech was able to get down low to deny the striker.
Schurrle had a chance for his second of the night with just over 20 minutes left to play, as Ba headed the ball forward for the goalscorer, but his shot was saved.
The visitors seemed to up their game as the final 15 minutes approached as they looked to make sure of their spot in the last four, but Cech denied Edinson Cavani before the Uruguayan blasted a shot over.
However, a late move from the home side saw the ball fall to Ba, to slot the ball in, giving Chelsea the advantage on away goals.
Cech had to make a series of late saves as PSG pushed for a last-gasp goal, but the Czech kept the ball out to see his team through to the last four.
Chelsea will be without Ivanovic for the first leg of their semi-final though, as he picked up a booking during the second half.
Source: www.sportsmole.co.uk
