Raul Jimenez put Wolves into the lead just before the hour mark, but Hazard broke the visitors' hearts with an injury-time effort from distance which found the bottom corner.
However, Chelsea remain sixth in the standings after more dropped points at their home ground, while Wolves open a one-point advantage over Watford in seventh place.
Chelsea went into the game having improved in the final third over their last three fixtures, but Maurizio Sarri's men were frustrated during the opening 45 minutes by a disciplined defensive performance from Nuno Espirito Santo's side.
The Blues had over three quarters of possession but, despite their time on the ball, just one opportunity was created for Gonzalo Higuain after 20 minutes.
Wolves were offering very little going forward, but Diogo Jota did have a goal disallowed having handled the ball before firing a shot into the top corner from distance.
The same pattern of play continued after the restart as Wolves continued to frustrate their hosts, but the West Midlands outfit proceeded to deliver the sucker punch they were looking for by taking the lead after 56 minutes.
Jota collected the ball on the halfway line and exchanged passes with Jimenez before the latter was played through on goal.
Jimenez looked like he had taken too much time when entering the penalty area, but the Mexican's eventual shot deflected off Cesar Azpilicueta and rolled into the bottom corner.
Going behind sparked Chelsea into life, and Patricio had to be alert to keep out a low 20-yard strike from Higuain and a driven long-range effort from Pedro.
Chelsea remained on the offensive without creating any more opportunities, and even the introduction of Callum Hudson-Odoi and Willian failed to lead to a sustained spell of pressure being put on the Wolves backline.
The visitors were offering more of a threat on the break, but Chelsea went close with three minutes left as Willian saw a curling effort tipped wide of the far post by Patricio.
The fourth official indicated four minutes of added-on time, and Chelsea equalised soon afterwards to break Wolves' resilience as Hazard found a gap through a pack of players with a 25-yard shot which nestled into the bottom corner.
However, Chelsea will not be satisfied with a point which keeps them behind Manchester United and Arsenal, while Wolves will also be disappointed having fought so valiantly to keep Chelsea at bay for 90 minutes.
CHELSEA (4-3-3): Arrizabalaga; Azpilicueta, Rudiger, Luiz, Palmieri; Kante, Jorginho (Willian 72'), Kovacic (Loftus-Cheek 56'); Pedro (Hudson-Odoi 61'), Higuain, Hazard
WOLVERHAMPTON WANDERERS (3-5-2): Rui Patricio; Saiss, Coady, Boly; Doherty, Dendoncker, Moutinho, Neves, Jonny; Jota (Gibbs-White 82'), Jimenez (Traore 89')