Playmaker Hazard showed plenty of nice touches as usual in the Barclays Premier League contest, and it was his ball into the box in the 78th minute that set up Cesc Fabregas for the visitors' second goal.
But along with the Belgium international's creativity, Mourinho was also keen to praise the way Hazard - like the rest of the Chelsea side - handled the physical challenge Stoke posed at times.
The 23-year-old was on the receiving end of a painful-looking tackle early on from Phil Bardsley that earned the Potters defender a yellow card
Others might have considered it a sending-off offence.
Hazard was able to carry on until departing the field in stoppage time, after being brought down by Jonathan Walters, with an apparent ankle problem - the seriousness of which was unclear ahead of the Boxing Day home clash with West Ham
Asked about Hazard still going on to influence the game on Monday night after the bruising encounter with Bardsley, Mourinho said: "He did a lot and we need that.
"We played with (John Obi) Mikel and (Nemanja) Matic, so we lost one creative player.
"We had that stability in the team, and left to Hazard, Fabregas and Willian the responsibility to create, and they were not afraid to do that.
"They gave their bodies to the game and put themselves in every situation, and I think the kid (Hazard) was fantastic."
Mourinho - whose side went 1-0 up in the second minute through John Terry's header, and will spend Christmas three points clear of second-placed Manchester City at the top of the league as a result of the win - indicated he felt Bardsley should have been sent off for the challenge on Hazard.
But he also stressed the match had been a fairly fought one overall.
And Mourinho added: "If the tackle on him (Hazard) was a bad one, it was an isolated action.
"Then, after that, it was a difficult fight for the kid - but I think it was also a difficult match for Bardsley, because the kid is playing fantastically."
Meanwhile, Stoke are 13th and still struggling to find consistency this term, with their last three results being a win, a draw and a loss.
One way in which they have found continuity has been undesirable - Monday's game was the 11th league fixture in a row that has seen them fail to keep a clean sheet.
Potters goalkeeper Asmir Begovic admits that is something that needs addressing swiftly.
"We have to start keeping clean sheets," Begovic told Stoke City Player.
"We have been sloppy at times by switching off at key moments and that's been costing us lately.
"We obviously need to try to fix that going forward.
"If we can get positive results then everybody is happy, but keeping clean sheets certainly helps and we will attempt to solve that as quickly as possible."
Stoke's Boxing Day match is at 11th-placed Everton.
Source : PA
Source: PA