Arsene Wenger's side were on course to secure top spot and a possible easier draw in the last 16 after taking a 2-1 lead in the second half.
Having trailed to Edinson Cavani's first-half opener, the Gunners equalised through Olivier Giroud just before the break and went ahead in the second half thanks to a Marco Verratti own goal.
But Lucas equalised in the closing stages to ensure Arsenal and PSG, who had both already qualified for the last 16, will have to wait until the final round of group matches to settle their fight for pole position.
Arsenal, who travel to Basel for their last match on December 6, sit second in the group, level on points with PSG, who play Ludogorets in their final fixture.
However, PSG have the slight edge and destiny in their own hands because they have the better head-to-head record against the Premier League side.
"We had good spells in the game but we could not dominate. My concern is that we were 2-1 up and allowed them to come back at us. It's difficult to understand how easy we gave away a goal at a corner," Wenger said.
"We lack something in our creativity but we got a point. It might not be enough but you never know."
PSG boss Unai Emery added: "We still have to play matchday six but we are currently in top spot and of course that is important.
"I think we deserved a draw to help take top spot."
PSG threatened an early opener when sloppy Arsenal marking allowed Uruguay striker Cavani to win a header in the penalty area and Thiago Motta narrowly failed to turn the loose ball into the net.
Unable to shake off their lethargy, Arsenal fell behind in the 18th minute.
Motta slipped a perfectly weighted pass towards Blaise Matuidi and, with Shkodran Mustafi caught flat-footed, the winger was able to direct a low cross into the six yard box, where the sliding Cavani had the simple task of netting his fifth Champions League goal this season.
PSG's preparations had been disrupted when Ivorian defender Serge Aurier was stopped from entering the United Kingdom at the last minute.
UK authorities revoked Aurier's visa following his two-month suspended prison sentence for assaulting a police officer.
Despite that PSG were far superior to Arsenal, whose lone attack of note in the opening 44 minutes ended with Aaron Ramsey appealing in vain for a penalty after Thiago Silva's challenge
Arsenal, laboured as they were, conjured an equaliser out of nowhere on the stroke of half-time.
Mesut Ozil guided a pass into Alexis Sanchez and his sharp turn drew a lunge from Grzegorz Krychowiak.
It appeared the Pole missed Sanchez and the ball, but the Chilean still fell and referee Felix Brych awarded a penalty.
PSG were clearly irked by the decision and Cavani became embroiled in a spat with Ramsey, but Giroud ignored the fuss and stroked home the spot-kick to make it two goals in successive games after his equaliser at Manchester United.
Lucas almost restored PSG's lead with a free-kick that grazed the top of the crossbar early in the second half.
Arsenal's luck was in again as they went ahead in comical fashion on the hour.
A promising Arsenal attack looked to have foundered when Ramsey and Sanchez couldn't finish, but Marquinhos's panicked clearance cannoned into Verratti and rebounded into the net past bemused PSG goalkeeper Alphonse Areola.
PSG finally had some good fortune of their own to snatch an equaliser in the 77th minute as Lucas nodded a tame effort goalwards and Alex Iwobi, trying to head clear, deflected the ball into his own net when David Ospina would easily have saved.
Cavani should have won it for PSG, but he missed two golden opportunities in the final minutes.