The Blues were staring down the barrel of a costly defeat courtesy of Raul Jimenez's textbook counter-attacking goal in the second half.
Maurizio Sarri's side can only be as far as four points adrift of the top four after Manchester United visit Arsenal on Sunday, while Wolves miss out on a first league double over Chelsea since 1974-75.
Chelsea enjoyed a near monopoly in terms of possession in the first half, but clear-cut chances were at a premium.
Gonzalo Higuain did get in behind only to be easily foiled from a tight angle by Rui Patricio, while tentative claims for handball after a mis-control from Jimenez in the area fell on deaf ears.
Wolves had not managed an effort on goal let alone on target, but their patience was rewarded with a classic counter for the opener after 56 minutes.
Diogo Jota and Jimenez combined brilliantly in midfield before the former had the wherewithal to play in the Mexico striker, whose prodded effort hit Cesar Azpilicueta and squirmed past Kepa Arrizabalaga.
That sparked Chelsea into life and Pedro's dipping try tested Patricio, while Higuain just failed to get a touch from close range from the resulting corner.
A diving Patricio kept out Willian's bending effort but, just when it looked like Wolves were home and hosed, Hazard struck.
The Belgium forward – who was otherwise a peripheral figure – was afforded too much space and Chelsea's talisman clinically found the bottom-right corner from 20 yards for his 50th Premier League goal at Stamford Bridge.
What does it mean? Chelsea clinging on in race for fourth
Tottenham's untimely domestic wobble has blown the remaining two spots for the top four wide open. Defeat here could have seen Chelsea finish the day as far as five points off fourth, but Hazard's rescue act keeps Sarri's men firmly in the hunt.
Jimenez strikes against top six again
Jimenez has proved quite the scourge for the 'big six' this season. No player outside of those teams has been involved in more goals against them (six – four goals, two assists). His 12 Premier League goals are also the joint-most in a single campaign for Wolves, level with Steven Fletcher.
Chelsea failed to really penetrate the Wolves defence and Higuain was as culpable as anybody else for that fact. The Argentine striker showed some decent touches, but rarely posed a goal threat.
Key Opta Facts
50 – Eden Hazard has now scored 50 Premier League goals at Stamford Bridge; only Man Utd (5) have had more players score 50+ home goals in the competition than @ChelseaFC (also Lampard and Drogba). Exclusive. #CHEWOL pic.twitter.com/e1eXTmCGRN— OptaJoe (@OptaJoe) March 10, 2019
- After a five-game winning run against promoted sides at Stamford Bridge, Chelsea have now failed to win two of their last four such home matches in the Premier League.
- Wolves are now unbeaten in six league games in London this season (W3 D3), their longest such run in the capital in the top flight since November 1974 (11 games).
- Only Cesc Fabregas (six) has assisted more Premier League goals for Chelsea’s Hazard than Willian (five).
- Wolves duo Jota (one goal, two assists) and Jimenez (two goals, one assist) have direclty combined for each of their sides' last three Premier League goals.
Chelsea, leading 3-0 from the first game, will look to complete the job against Dynamo Kiev in Thursday's Europa League last-16 return leg, while Wolves – perhaps slightly deflated by the late goal – have an FA Cup quarter-final with Manchester United to prepare for.