With the game at The Hawthorns all but won with United 2-0 ahead courtesy of a couple of goals from Zlatan Ibrahimovic, Fellaini was brought on for captain Wayne Rooney after 83 minutes to help protect the lead and his introduction was met with warm applause from the travelling United faithful.
It was in stark contrast to last weekend's home win over Tottenham, when the 29-year-old was jeered by some United supporters for his costly mistake against Everton, where he gave away a late penalty in the 1-1 draw at Goodison Park.
Mourinho paid tribute to the fans and thanked them for not booing Fellaini again.
"The fans are fantastic," he told MUTV.
"They had just an impulsive reaction because of Marouane's naive reaction against Everton, but they know that Marouane is a guy that gives absolutely everything
Inside the dressing room people love the guy and it's important for him to get that good feeling of knowing the fans are behind him."
As an additional thank you, after the win at The Hawthorns the Manchester United manager told his players to throw their shirts into the crowd and give them to Reds fans as a Christmas present.
"I told them to do that, [it's] Christmas time
A shirt for a fan, coming direct from the game with sweat, means a lot," said Mourinho in his post-match press conference.
"For them [United players], it is just another shirt that they would give to the kit man, or give to some friend, or they change with some West Bromwich Albion friends
I think to a fan it means a lot.
"It is a pity that not everyone can get one, but, for the ones who get it, I think it is a great feeling."
West Brom boss Tony Pulis is looking to add "one or two" players to his squad when the transfer window opens and hopes Albion can maintain their position in the Premier League over Christmas in order to improve their chances of making signings
Pulis, whose side are seventh in the table ahead of Sunday's fixtures, said: " We've got three points out of three difficult games against Chelsea, Swansea and Manchester United
"Now what we have to do is make sure we hang in there until the window opens and fingers crossed we can add one or two to the squad
"That's what we need to do, add one or two to the squad and keep things ticking over and going in the right direction."
Source : PA
Source: PA