Goals by substitutes Andre Schurrle and Demba Ba at Stamford Bridge proved to be enough for the Blues to win the tie on away goals after the quarter-final had ended 3-3 on aggregate.
PSG controlled the first 30 minutes, slowing the pace of the match down and causing the Chelsea defence numerous problems with their rapid counter-attacks.
The Blues did not create their first opening until just before the half-hour mark when Frank Lampard’s deflected free-kick almost caught Salvatore Sirigu out but the PSG keeper did well to punch the ball away for a corner.
Jose Mourinho’s side took the lead in the 32nd minute though when David Luiz flicked the ball on to Schurrle, who had earlier come on as a substitute for the injured Eden Hazard. He guided his shot from almost on the penalty spot past Sirigu.
Five minutes later Gary Cahill wasted a great chance to make it 2-0 when he miskicked a shot horribly wide from ten yards out after Lampard’s free-kick had caused mayhem in the PSG area.
Early in the second half the French side were saved by the crossbar twice in two minutes.
On the first occasion, the lively Schurrle rattled the woodwork with a great strike from just inside the area with Sirigu beaten before Oscar’s free-kick beat the wall only to also come back off the bar.
Edinson Cavani had the opportunity to send Laurent Blanc’s side through when he latched on to Yohan Cabaye’s ball forward only to then lift his shot over the bar when it seemed easier to score.
It proved to be a costly miss as, with 87 minutes on the clock, Ba lifted the ball into the roof of the net from close range after a goalmouth scramble to send Mourinho’s side into the semi-finals.
Burnley midfielder Jack Cork is confident his side can reach the Europa League but expects a stern test in qualifying.