Branislav Ivanovic's first-half header put the Premier League leaders in front in Tuesday's round of 16 first leg, but that was harsh on injury-hit PSG - unbeaten at home in UEFA competition since 2006.
Laurent Blanc's side suffered a heartbreaking quarter-final defeat against Chelsea on away goals last season - after winning the first leg in the French capital 3-1 - and Ivanovic's opener was a blow to their hopes of gaining revenge.
The Ligue 1 champions were deservedly level just nine minutes into the second half, though, when Uruguay striker Cavani rose unmarked to head home.
PSG looked the more likely to fashion a winner but were routinely denied by off-target finishing and returning Chelsea goalkeeper Thibaut Courtois, whose goal they will certainly have to breach again in second leg at Stamford Bridge next month.
Counting the cost of a dramatic draw against Caen at the weekend, PSG were without Yohan Cabaye, Serge Aurier and Lucas Moura but made a composed start nevertheless as Blaise Matuidi drew Courtois into action with a firm header.
Courtois had to deal with Zlatan Ibrahimovic's header soon after and Cavani also worked the Belgian with a similar effort after Chelsea were caught napping from an Ezequiel Lavezzi corner 11 minutes before the break.
Chelsea were boosted by the return of Diego Costa and Cesc Fabregas, but Salvatore Sirigu had been little more than a spectator until he was forced to pick the ball out of his net nine minutes before the break.
Much is made of Chelsea's attacking prowess, but it was there defenders who combined for the opening goal as John Terry's cross was flicked on by Gary Cahill and the unmarked Ivanovic was on hand to head home.
PSG must have wondered how they were behind at the break, but they were level early in the second half when Cavani capitalised on some slack marking from Cahill to head home Matuidi's inviting cross from six yards out.
The hosts were dominant and Courtois did well to palm away a left-footed strike from Ibrahimovic on the hour before Cesar Azpilicueta blocked Lavezzi's effort following up.
David Luiz came close to putting PSG in front against his former club, but the Brazil defender's header took a slight deflection before landing on the roof of the net.
As PSG searched for an advantage, Cavani prodded just wide and Courtois once again came to the rescue to claw away Ibrahimovic's downward header – putting Chelsea firmly in the driving seat for a place in the last eight.
