The Slovenian upstarts, destroyed 6-0 by Chelsea at Stamford Bridge two weeks ago, took the lead in the 50th minute when Macedonia winger Agim Ibraimi curled in a spectacular left-foot shot from the edge of the box.
Maribor, buoyed by a noisy crowd, swarmed all over Jose Mourinho's side and had a great chance to make it 2-0 on the hour when unmarked teenager Luka Zahovic blazed the ball over the bar from six metres with an open goal at his mercy.
Chelsea then upped the tempo and Nemanja Matic equalised with a tap-in at the far post after captain John Terry had headed on a right-wing corner from Cesc Fabregas in the 73rd minute.
The Londoners spurned an excellent opportunity to grab all three points when Eden Hazard was tripped in the box with four minutes to go. The Belgian picked himself up to take the penalty but his effort was saved by Jasmin Handanovic.
Group G leaders Chelsea still look well placed to qualify for the knockout stages with eight points from four games.
Schalke 04 have five points after losing 4-2 at Sporting Lisbon (four) on Wednesday and Maribor (three) are also in with a chance.
A grim-faced Mourinho, who brought on Diego Costa and Oscar for Andre Schuerrle and Willian at halftime and also replaced Filipe Luis with Ramires 11 minutes into the second half, was clearly unhappy with his side.
"We didn't play well in the first half ... and when you don't play well for 90 minutes you take a risk," the Portuguese told Sky Sports television.
"In the last 30 minutes we started to play really well with intensity and desire and we had a lot of chances but their keeper was magnificent."
FRONT FOOT
Chelsea, runaway leaders in the Premier League, started the game on the front foot with the unmarked Kurt Zouma heading over from six metres and Didier Drogba, making his 100th career appearance in a UEFA competition, forcing Handanovic into a sprawling stop.
The longer the half went on, however, the more pedestrian the passing became from the visitors.
Ibraimi's stunning left-foot drive sent the crowd wild and Maribor, back in the Champions League group stages after a 15-year absence, sensed victory but Hazard, Oscar and Fabregas suddenly took hold of proceedings.
The Londoners continued to drive forward after Matic's equaliser and Handanovic performed heroics when he went full length to deny Hazard after the Belgian burst clean through the home defence.
The Maribor keeper then tipped over a powerful volley from Costa who also had a goal chalked off because Fabregas was offside.
Hazard then saw his spot kick saved by Handanovic - the winger's first missed penalty in his two and a half years at Stamford Bridge.
At the final whistle Chelsea could console themselves in the knowledge they had equalled their best-ever start to a campaign set in season 2005-06.
