André Schurrle, only on the pitch due to an injury to Eden Hazard, fired Chelsea into a first-half lead before Ba scored the decisive goal just a few minutes after Edinson Cavani missed a golden chance for the visitors.
Chelsea enjoyed a couple of half-chances, notably through Samuel Eto'o who saw an effort deflected wide. PSG showed the danger of their pacy front three on the counter. Ezequiel Lavezzi broke away from his markers to go on a fine run to set Lucas Moura free, but the Brazilian could not quite find Cavani in the area.
Chelsea suffered a huge blow to their chances in the tie -- and perhaps the Premier League -- when Hazard limped off after just 17 minutes with a mysterious injury. The incident proved significant because his replacement, Schurrle, went on to have a big influence in the rest of the game.
Chelsea came close to taking the lead, despite not looking particularly threatening, when Frank Lampard's free-kick was almost deflected in. The midfielder could only thump his set-piece into the wall, but Stephane Sirigu had to react with lightning speed as the ball arrowed towards the opposite corner.
Chelsea soon did have their goal, however, courtesy of a Branislav Ivanovic long throw and some appalling marking from the visitors. David Luiz flicked on the Serbian's launched ball and Schurrle was in an ocean of space to turn and fire past Sirigu from close range.
PSG then seemed to suffer another setback when Thiago Silva went down after a collision with Eto'o, but the Brazilian soldiered on for the rest of the half despite a stretcher being brought on. The Parisians were perhaps slightly fortunate to avoid further calamity when Verratti, already on a yellow card, escaped with a questionable penalty claim after he collided with Schurrle in the area.
PSG made it to halftime, but still looked distinctly second-best and a shadow of their usual selves in the second half. They remained ahead afterwards only by the finest of margins after a counterattack led to a ferocious Schurrle effort striking the bar. Oscar did the same from a free-kick just a minute later.
Laurent Blanc reacted by withdrawing the disappointing and increasingly erratic Verratti for Yohan Cabaye, which seemed to momentarily improve PSG's control of the game. José Mourinho, with time ticking away for Chelsea, opted for an attacking substitution by replacing Lampard with Ba, and Blanc followed suit, sending on Javier Pastore for Lavezzi.
As the end of the game approached, Chelsea narrowly avoided a knockout blow when the substitute Cabaye picked out Cavani's run, but the Uruguayan, again having a poor match after a dire showing in the first leg, blazed over with plenty at which to aim.
Chelsea were looking increasingly unlikely to get anything out of the game, yet with just a few minutes of normal time remaining, Ba -- one of three strikers Mourinho had sent on -- found a way through, turning in a deflected effort during a scrappy attack on the visitors' goal and sending Stamford Bridge wild with delight. PSG had little time to find a goal, and Marquinhos had the only real chance from a corner, but Petr Cech made a fine save to keep Chelsea's lead until the final whistle.
It was not pretty, and PSG were surprisingly awful, but Mourinho's team nonetheless overcame a difficult first-leg scoreline to book their place in the semifinals. Over to you, David Moyes.
Chelsea: Cech, Ivanovic, Cahill, Terry, Azpilicueta, Luiz, Lampard (Ba 66'), Willian, Oscar (Torres 81'), Hazard (Schurrle 18'), Eto'o.
Goals: Schurrle 32', Ba 87'.
Paris Saint-Germain: Sirigu, Jallet, Alex, Thiago Silva, Maxwell, Verratti (Cabaye 55'), Thiago Motta, Matuidi, Lucas Moura (Marquinhos 84'), Cavani, Lavezzi (Pastore 73').