The 35-year-old former Sweden international found the back of the net two minutes from time at Selhurst Park after James McArthur cancelled out Paul Pogba’s opening goal.
The former Paris St Germain forward took his tally to 14 for the season and Mourinho said: “I knew the character because at this age it is the passion, the personality that plays.
“The quality is there, I knew he could do well here. I told him that England is not the best for holidays, you come here for the most difficult league in the world, his decision to come here was based on that.
“His motivation, his goals, he is really good.”
United’s second Premier League victory in a row takes their unbeaten league run to seven and Mourinho believes that his players’ efforts have merited the turn-around in results.
He added: “I think the players they deserve that.
“That is what you have to do. Even if this game finished 1-1, I would have the same feeling, it is difficult.
“The players they reached some limits, they were tired, there were some injuries, Zlatan told me he was tired but they gave everything they could.
“The boys they did phenomenal against a difficult team. The boys deserved the late happiness.
“Two victories means six draws. The reality is that I focus on performances, they have been very good for a long time.
“The players deserve this happiness, home and away.
“We are looking at teams that desperately need points to get out of relegation.”
The game had a number of controversial moments including Pogba’s goal, which the Frenchman converted from an offside position after Ibrahimovic appeared to handle the ball in the build-up.
Marcos Rojo could also have been sent off for a two-footed tackle but neither Mourinho nor Crystal Palace manager Alan Pardew were keen to dwell on the decisions made by referee Craig Pawson.
Mourinho said: “(Pawson) is good. He is one of the good, young referees.
“If he made mistakes then that is unfortunate but we need to support young referees.”
Pardew added: “I thought the first goal was a call the linesman should have seen. I think the referee played the game aggressively, it could have flowed a lot more.”
The Eagles boss was disappointed his side did not get anything out of the game, as the result sees them slip to 16th in the league, but he admits there were a number of errors in defence.
He said: “I have to look at the team and say they were committed.
“Defensively I thought we could have done a little better in the first half.
“Second half we had a good spell, got a great goal and it was a shame that we couldn’t kick on.
“In the end we were undone by two great players.
“I think Christian (Benteke) had a quiet night tonight, our hold-up play could have been better.
“We had a bit more aggression. I feel for them because they deserve a break.”