Chelsea led 1-0 at half-time in Paris thanks to Branislav Ivanovic's header but PSG dominated the second half with Edinson Cavani levelling in the 54th minute.
The hosts were denied a winning goal, however, with Courtois putting in an impressive shift.
Having thwarted Cavani in the first half, the Belgian spread himself impressively to parry an effort from Zlatan Ibrahimovic, before denying the Sweden striker's firm header in stoppage time.
"Without their goalkeeper, we would have won this game. He [Courtois] was great," David Luiz said after the match.
"We did well. They got one goal from one opportunity but I think we can go through over there."
Chelsea eliminated PSG in the Champions League quarter-finals last season, turning around a 3-1 loss in the French capital with a 2-0 victory at Stamford Bridge.
The round of 16 second leg in London will be held on March 11.
