Ezequiel Lavezzi had earlier scored one goal and set up another to leave the Blues with it all to do going into next Tuesday's Champions League quarter-final second leg at Stamford Bridge.
PSG got off to the best possible start as, in the third minute, they took the lead when John Terry's poor headed clearance dropped to Lavezzi, who fired a rising left-footed shot past Petr Cech.
Midway through the first half Lavezzi went close to doubling PSG's lead when he beat Gary Cahill for pace, but the impressive Argentinian could then only fire his shot into the side-netting.
The visitors were level in the 27th minute though when Eden Hazard sent Salvatore Sirigu the wrong way with his right-footed penalty, after Oscar had been fouled by Thiago Silva.
Chelsea went close to taking the lead five minutes before the interval when Hazard's volley from a tight angle hit the post with the PSG goalkeeper beaten.
However, on the stroke of half time, Chelsea had to survive a penalty appeal when Edinson Cavani went down under Cahill's challenge, only for the referee to wave play on.
At the start of the second period an unmarked Lavezzi got his head to Blaise Matuidi's pinpoint cross, but the ball flew just over Cech's goal.
Just past the hour mark, David Luiz tried to get out of the way of Lavezzi's curling free-kick but could only turn the ball into his own net.
Zlatan Ibrahimovic, who struggled to make any kind of impact on the game, had to be substituted midway through the second half with what appeared to be a thigh injury, which may keep him out of the second leg.
However, PSG go into the second leg with a two-goal advantage as, deep into stoppage time Pastore jinked his way past three Chelsea players and into a shooting position, before beating Cech at his near post.