Romelu Lukaku scored twice in the first half to fire United back to winning ways, although the Red Devils also missed a penalty and squandered a number of other opportunities throughout a dominant display.
The visitors had to see out the game with 10 men at Turf Moor following a red card for Marcus Rashford, but Mourinho was delighted with his side's all-round performance and reserved special praise for his defenders.
"I think it was a very, very good performance with a result which was short," Mourinho told BBC Sport.
"They played very well as a team, and there were very good individual performances and we should score many more goals. The result shouldn't have been open until the last minute. There were lots of good performances but [Marouane] Fellaini was fundamental, together with [Chris] Smalling and [Victor] Lindelof. Luke Shaw had a good performance and there were many others, too.
"We lost so many chances and Joe Hart made important saves. I don't remember such a comfortable performance as we've shown in the last two matches."
Mourinho also criticised Rashford for his role in the sending-off, describing the striker as a "naive boy".