In a fixture that had looked a tricky prospect but which they controlled admirably, the Blues went 1-0 up in the second minute through John Terry's header before wrapping up the win via Cesc Fabregas' scuffed effort with 12 minutes remaining.
Things got feisty at times, but Chelsea coped well when Stoke got physical.
And the Portuguese, whose table-toppers will spend Christmas three points clear of second-placed Manchester City, said: "To win here, we had to play a very good game.
"We did it because we adapted well to their style of play
When they had the ball, we adapted well to them
When we had the ball, we tried not to lose our identity.
"Obviously to score a goal at the beginning is important, but not so much in this stadium because Stoke are always strong and the crowd is always behind them
The team are mentally strong, they believe and they have good players.
"So it was a very difficult victory
It is a victory that means a bit more than just the three points, because to win here, you need to show more than just your quality.
"The players coped well - our creative players were not afraid to try to create, and our defensive players were very solid.
"Only with a great team performance is it possible to be successful against Stoke."
One particular moment of physicality came early on when Stoke defender Phil Bardsley put in a rash tackle on Chelsea playmaker Eden Hazard, the Potters man appearing perhaps somewhat lucky to only be punished with a yellow card.
Mourinho suggested Bardsley should have been sent off, but stressed he felt the match overall, while "aggressive", had been fair.
He said: "From my position, it looked like a red card, but I don't know.
"What I know is that if it was a bad tackle, it was the only one - the game was clean
It was aggressive, but good - the referee kept it under control and the players were fair.
"There were good fights, physicality, lots of duels, but I think the game was perfectly clean and correct.
"So if it was a red card, it was an isolated action."
Mouriho felt Hazard, who set up Fabregas' goal, had been "fantastic" and added: "There was one action that showed clearly for me what he (Hazard) is.
"Bardsley was injured and Eden, a few minutes after being tackled that way, is the one who puts the ball out
I wouldn't do it to a guy who kicked me a few minutes before!"
Mourinho also had praise for centre-back Terry, who scored his first Premier League goal since December 2013 and has now netted in 15 consecutive top-flight seasons.
The manager said of his captain: "When he is on the pitch he is always a threat.
"But more important for me than the goal is the way he is playing this season, again.
"When I came here (in the summer of 2013) he was a bit in trouble, his career was a bit up and down and he was not playing regularly for Chelsea.
"Now in the last two years he is playing every game, and for me he is at the same level from 2004-2007 when I was here (as manager before).
"I think he adapts well to our training methodology - it's a good way for a person with his body type to feel sharp and fast and in good condition
After that it's happiness.
"When you're happy and confident it's easier in any job.
"He knows the way I trust him, and he feels confident and happy and he's playing very well."
Stoke boss Mark Hughes, whose side are 13th, felt they had applied themselves well after conceding Terry's header.
Hughes said: "It was the worst possible start for us - the one thing you don't want to do is concede early to a top-quality side like Chelsea.
"But credit to us, I thought we stuck at it and kept probing.
"It was difficult, because Chelsea were happy to protect the initial lead - they are quite able to take the sting out of games, which comes from experience.
"We had to deal with that and be mindful of them threatening too, but they didn't have too many chances.
"Then we had a decent period second half, but in the end they had a little bit of quality enabling them to get the second goal
That took the game away from us."
Hughes confirmed Potters striker Peter Crouch had come off due to a neck problem he is hopeful will not keep him out of their Boxing Day trip to Everton, while it remains to be seen if Hazard can play against West Ham that day after he was substituted late on with an apparent ankle injury.
Source : PA
Source: PA