Romelu Lukaku scored twice, Anthony Martial netted a penalty and Henrikh Mkhitaryan hit the fourth as the Red Devils maintained their 100% record in Group A.
The Old Trafford side had won just one of their previous 10 away games in the competition, but two goals in the opening 18 minutes set up a very comfortable night at the VEB Arena.
“The important thing is two matches, six points and a good position in the Champions League,” said Mourinho, whose side beat Basel 3-0 in their opening game.
“Four more matches to play but we started really strongly and we are almost there.
“I think we surprised them with our attitude and we were really strong, and we killed the game. They did not look as good as they are but I think that was because of us.”
Lukaku has now scored 10 goals in nine games since joining United from Everton in the summer.
“I have to admit he is scoring really important goals almost every game,” said Mourinho.
“We know that he is a very good player, he can score lots of goals, and playing in a team surrounded by quality players it is even easier to do that.”
Four minutes in the Belgian striker headed in a cross from Martial, who went from provider to goalscorer by converting a penalty after Mkhitaryan was brought down.
And, in the city in which their third and most recent European Cup triumph came in 2008, United effectively ended the game as a contest on 26 minutes.
Aided by some dreadful defending from the home side, Lukaku slotted in his second from a couple of yards out.
Mkhitaryan added the fourth from close range and United could have scored more – Lukaku was twice denied by brilliant stops from Igor Akinfeev, who also thwarted Jesse Lingard.
Lukaku said: “I just work hard and will keep on going. The team is doing well but we must improve. I just want to win trophies.”
CSKA did have chances, with the excellent David de Gea twice saving sharply from Alan Dzagoev and tipping over a Fedor Chalov shot.
And Konstantin Kuchaev slid in a well-taken consolation late on to give the boisterous home fans something to cheer.
In the group’s other game, former Norwich striker Ricky van Wolfswinkel scored a penalty as Basel trounced 10-man Benfica 5-0.
