The Slovenians were unrecognisable from the side beaten 6-0 by Chelsea two weeks ago and claimed a deserved lead when Agim Ibraimi curled in a beautiful shot into the top corner five minutes into the second half.
Chelsea boss Jose Mourinho had already reacted to a poor first-half showing by his side at the Stadion Ljudski vrt by making a double substitution at half-time, introducing striker Diego Costa and Oscar.
Luka Zahovic missed a fine chance to double the advantage and enhance Maribor's claims of inflicting Chelsea's first defeat of the season, before Nemanja Matic's close-range effort 17 minutes from time which saved the Blues' blushes.
Maribor goalkeeper Jasmin Handanovic saved well from Hazard and Costa, who had the ball in the net after 79 minutes, only for the strike to be ruled out for offside.
Hazard was then fouled for an 86th minute spot-kick, but the Belgian's effort was too central and Handanovic saved.
Mourinho was less than impressed by the performances against Shrewsbury and QPR and it was another insipid showing.
It was not the warm-up the Premier League leaders would have been hoping for ahead of a return to domestic duty at Liverpool on Saturday lunchtime.
While Liverpool made wholesale changes for their Tuesday night trip to European champions Real Madrid, Mourinho kept his to four for a match against a team merely pleased to have reached this stage
Maribor's Champions League campaign began on July 15 - a day before the Blues' first pre-season fixture - and had already upset Celtic to reach the group stages.
Mourinho described the Stamford Bridge contest as a "fake" as Chelsea took every chance which fell for them, something his side ordinarily fail to do.
Two weeks on, Petr Cech made his fourth start of the season after being displaced by Thibaut Courtois as first-choice goalkeeper.
Kurt Zouma, Didier Drogba and Andre Schurrle also came in following the 2-1 defeat of QPR, for Gary Cahill, Costa and Oscar.
Zouma could have given the Blues, playing in yellow, the lead but headed wide from Fabregas' cross after Maribor half-cleared a corner.
A deflected Drogba shot was saved by Handanovic as Chelsea pressed forwards again, with Maribor packing bodies behind the ball and playing on the break.
Maribor breached the Chelsea defence, but Zouma scrambled clear a Sintayehu Sallalich shot after Zahovic's pull-back.
World Cup winner Schurrle has struggled to impress since returning to club duty, missing a host of chances against Bolton, spurning a sitter at Sporting Lisbon and doing little to enhance his hopes of regular game time at Shrewsbury last week.
The Germany forward and was unable to convert a straightforward opening from a deflected Willian cross, but his embarrassment was tempered by an offside flag.
Drogba and Hazard were denied and Mourinho was told to "sing up" and "give us a song" by the travelling support.
They were references to his comments on the atmosphere against QPR being unsatisfactory and he will have been less than impressed to reach half-time level.
His reaction was to send for reinforcements in the shape of Costa and Oscar, with Willian and Schurrle hauled off.
Chelsea soon fell behind, though, as Ibraimi, in the right channel, turned back on to his left foot and struck an unstoppable shot into the far corner of Cech's goal.
Ramires replaced Filipe Luis in Chelsea's third change as Mourinho switched to three at the back.
The tactical switch almost came at a cost as Maribor left-back Mitja Viler roared forward and crossed dangerously to the back post, where Zahovic missed a glorious opportunity.
Drogba was unable to get a header on target and Oscar's run at the Maribor defence ended with him prone on the floor, appealing in vain for a penalty.
The Brazilian flashed a deflected shot wide and Chelsea equalised from the resulting corner by Fabregas.
John Terry headed the ball down and Matic thumped it in from close range.
Chelsea continued to press forward and Oscar found Hazard, who was denied when one-on-one by Handanovic.
The goalkeeper acrobatically tipped over Costa's volley from Hazard's cross and was then beaten by the Spain striker, only for an offside flag to deny Chelsea.
Danger lurked and Tavares fired wide on the counter attack.
With the game stretched, Hazard took it upon himself to make something happen and his trickery saw him fouled by Viler.
However, the Belgium playmaker saw his spot-kick saved as Maribor secured a deserved draw.
Source : PA