The Belgian's tame effort from 12 yards was parried away easily by Jasmin Handanovic as the Slovenian champions held on to claim a deserved point against the lacklustre Blues
The confident Slovenians took a deserved lead five minutes into the second half when Agim Ibraimi curled superbly past Petr Cech, and Luka Zahovic missed a gilt-edged opportunity to double their advantage soon afterward.
Chelsea rallied and Nemanja Matic poked in the equaliser on 73 minutes before Hazard won himself the chance to complete the comeback from the penalty spot, only for Jasmin Handanovic to parry away his tame effort.
The Blues headed into the encounter knowing victory could secure their place in the last 16 should Sporting fail to beat Schalke.
However, the Portuguese side had few difficulties brushing aside Roberto Di Matteo's men 4-2 in Lisbon as Chelsea toiled - although the Premier League leaders remain three points clear at the summit of Group G with two games remaining.
Chelsea began strongly and almost took the lead in the eighth minute, Kurt Zouma heading narrowly wide after being picked out by Cesc Fabregas' clever cross.
Didier Drogba, selected in order to give the injury-plagued Diego Costa a rest, was next to threaten when he saw his deflected effort force a good reaction save from Handanovic.
Yet Chelsea were thankful just to be on level terms soon after, Zouma denying Sintayehu Sallallich with a goal-line clearance after Marcos Tavares' superb surging run had opened up their defence.
That prompted a much better spell for the hosts, who were suddenly showing more intent.
Sallalich was looking the most likely to score, forcing a solid save from Petr Cech - in for Thibaut Courtois - with an effort from range.
The visitors came back into the game as the half wore on, the ever-dangerous Hazard forcing Handanovic into a smart stop.
Chelsea would lose momentum after half-time, however, as Maribor took a surprise lead.
Ibraimi grabbed the goal, superbly side-footing beyond a helpless Cech from just outside the area after Zouma's clearing header had inadvertently picked out the winger.
Mourinho had introduced Costa at the interval in an attempt to kick-start his team's performance.
However, the Spain striker struck his first chance wildly over the crossbar as Chelsea failed to find an immediate response.
Chelsea were almost two behind in the 59th minute, Luka Zahovic hitting over with the goal gaping after being picked out by Mitja Viler's excellent cross.
Perhaps awoken by that scare, they roared back impressively with Oscar curling an effort narrowly wide.
And Chelsea got back on level terms in the 73rd minute when Matic tapped in on the line after John Terry had flicked on Oscar's corner.
The London club should have gone ahead not long after, with Hazard denied by Handanovic when one-on-one with the goalkeeper.
And further frustration was to come for Mourinho, as Hazard spurned a golden opportunity from 12 yards after being brought down in the area by Viler.