The defending champions enjoyed much of the possession but were largely unproductive during the first half of Sunday's match.
Luis Enrique's team played better after the interval and PSG finally created chances as Nuno Mendes levelled the scores following Nice defender Ali Abdi's first-half opener.
Lagging three points behind unbeaten Monaco before kickoff, PSG were too timid to hope for a better result on the Riviera.
Dembele started the match after being left out of the squad that lost 2-0 to Arsenal in the Champions League midweek.
Luis Enrique, who had blamed Dembélé for a perceived lack of commitment, was criticised after the loss for not selecting the France star.
Nice took a deserved lead in the 39th minute when Abdi controlled the ball on the edge of the box and followed up with a left-footed shot that took a slight deflection and went in.
Luis Enrique replaced the largely inefficient Randal Kolo Muani with Lee Kang-in, who greatly improved the connection between PSG's midfield and their attack in the second half.
Dembélé's effort in the 47th was parried away by Nice goalkeeper Marcin Bułka, who was however powerless five minutes later when Nuno Mendes equalised with a deflected shot from outside the box.
Monaco have a two-point lead over PSG, with third-place Marseille five points off the pace.
Seven-time French champions Lyon continued their recovery with a fourth straight win in all competitions by beating Nantes 2-0.
The match was marred by fan violence and Lyon said the clashes that broke out at Groupama Stadium were "unworthy" of the club.
A goal from Nicolas Tagliafico and an own-goal from Nantes defender Nicolas Pallois earned Lyon their third win in seven league matches, giving the club some room to breathe at five points above the relegation playoff spot.
Tagliafico put the hosts in the lead in the 22nd minute from Saïd Benrahma's cross for his first goal this season.
Nantes wasted several occasions to level and were punished after the interval when Pallois accidentally beat his own goalkeeper as he tried to defend a cross from Corentin Tolisso.
Hosts Reims moved up to fourth place with a 4-2 win over Montpellier.
The Champagne side took the lead in the sixth minute with a header from captain Marshall Munetsi.
Keito Nakamura exploited a poor clearance to show his dribbling skills and make it 2-0 with an impressive strike. Oumar Diakité and Teddy Teuma scored Reims' other goals while Arnaud Nordin had a brace for Montpellier.
The southern team remained in the relegation zone with the worst defensive record in the league, having already conceded 21 goals.
In other matches, Brest followed up their 4-0 midweek win over Salzburg in the Champions League with a 2-0 defeat of Le Havre, and Lens drew 2-2 at Strasbourg.
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