The Premier League leaders, unbeaten in 16 matches in total this season, were lacklustre in the first half and a shock appeared to be on the cards when Agim Ibraimi curled in a brilliant left-foot shot for the Slovenians after 50 minutes.
Unmarked teenager Luka Zahovic almost made it 2-0 when he blazed the ball over the bar from six metres 10 minutes later and that signalled a Hazard-inspired onslaught from Chelsea.
Nemanja Matic tapped in the equaliser after 73 minutes and the Londoners went on to create a series of chances in the closing stages including a rare missed penalty from Hazard after yet another mazy dribble from the Belgium winger.
“For me Eden Hazard was fantastic,” Mourinho told Sky Sports television after Chelsea cemented their place at the top of the group with eight points from four matches.
“He may have missed a penalty but he was still by far the best player in my team.”
Mourinho was so unhappy with his team’s display in the first 45 minutes that he made two changes at halftime, bringing on Diego Costa and Oscar for Andre Schuerrle and Willian.
Not content with that reshuffle, he also swapped left back Filipe Luis for Brazil midfielder Ramires 11 minutes into the second period.
“In the first half we weren’t good,” he said. “We played very slow with no intensity or creativity, it was easy for Maribor to control the game.
“I tried to improve my team and I think I was successful because in the second half the team was much better.
“We played very well but then they scored which made the game more difficult for us. After that I think we were magnificent, creative, fast, dynamic, lots of chances to score,” said Mourinho.
“Sometimes surprises can happen when players aren’t fully focussed. Only when Maribor scored did they realise the game was in danger.”
Chelsea also had a late Costa goal chalked off after Cesc Fabregas was adjudged offside.
“We scored two goals, two very good goals, but the second the referee disallowed,” said Mourinho.
“It was a clear goal so normally we should have won. We have to accept it and praise a fantastic stadium with lots of enthusiasm for a fantastic night.”
Chelsea’s next Champions League match is a trip to Schalke (five points) in three weeks’ time and a victory there will secure their place in the last 16.
Maribor, back in the group stages for the first time in 15 years, can also still qualify for the knockout rounds for the first time.
The Slovenians, who have three points from four games, travel to Sporting (four) for their next match.
(Writing by Tony Jimenez, editing by Greg Stutchbury)