A second-minute header from John Terry and Cesc Fabregas' finish in the second half gave the Londoners a three-point lead at the top of the table over Manchester City at Christmas.
But it was the manner of the victory that pleased Mourinho the most with Chelsea forced to win a physical battle. "To win here we must play a very good game and we did it because we adapted well to their style of play," said the Portuguese.
"When we had the ball we tried not to lose our identity and play our game. They [Stoke] are always strong in this stadium, the crowd is always behind them. They have good players and a good bench. It was a very difficult victory.”
Coach all praise for Terry
Mourinho saluted captain Terry who scored in the Premier League for a 15th consecutive season.
"He is extremely dangerous in set pieces and is a very good player in the air," he added.
"More importantly is the way he has been playing this season again. When I came here last year he was in a bit of trouble, his career was a bit up and down. He was not playing regularly for Chelsea.
"But suddenly in the last two years, he is playing basically every game and for me at the same level as when I was here 2004-2007.”
Stoke full back Phil Bardsley was booked for a bad tackle on Belgian star Eden Hazard in the first half but Mourinho, who was incensed at the time, thought it should have seen him sent off.
"From my position and in the flesh it looks for me a red card but I don't know," said Mourinho.
"What I know is that if it was a bad tackle it was the only one. It was a clean game but an aggressive one. The referee kept the game under control. The players were fair.”
His Stoke counterpart Mark Hughes took heart from his side's display as they matched Chelsea all the way until Fabregas' strike on 78 minutes.
"It was the worst possible start," said Hughes. "You don't want to concede early to a top quality side like Chelsea.
"We did not offer them too many clear cut chances. It looked like we might get back on level terms."
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