Mitrovic’s early penalty put the hosts ahead – the Serbian striker was controversially judged to have been fouled after what seemed a well-timed tackle from Kyle Bartley.
Mitrovic gratefully scored his side’s second shortly before half-time as he slid home from Robert Snodgrass’ weak backpass.
The Baggies had Darnell Furlong sent off with 20 minutes to go before Mitrovic wrapped up the win with a close-range effort eight minutes from full-time.
Fulham had Tosin Adarabioyo sent off with five minutes to go for a studs-up challenge on Grady Diangana, but by then the result was safe.
The win opens up a four-point gap between Fulham and West Brom, who will remain in third place after this weekend.
Marco Silva’s side are now only two points off Championship leaders Bournemouth before the Cherries’ evening kick-off at Reading.
Fulham started the first half well, Harry Wilson seeing an effort deflected wide as Neeskens Kebano and Antonee Robinson found some joy down the left.
But the game’s controversial moment came after 18 minutes when Mitrovic dramatically went down in the penalty area having been played through by Bobby de Cordova-Reid, after Dennis Odoi had won the ball off Karlan Grant in midfield.
Referee Michael Salisbury felt Bartley had fouled the striker when replays appeared to show that he made little contact with the Serbian and had played the ball with the outside of his right foot – Mitrovic stepped up to fire the penalty low into the right corner for his 16th goal in 14 appearances this season.
The goal appeared to inspire the Baggies – Grant fired across the face of the goal soon after the restart, Bartley twice went close with headers and Marek Rodak saved a Matt Clarke header.
But West Brom had no complaints with Mitrovic’s surprise second – Snodgrass could only apologetically hold his hands up after putting the striker’s 17th goal of the season on a plate for him as the visitors tried to play out from the back.
Valerien Ismael’s men came out strong after the restart as they put Fulham under pressure in midfield and came close to pulling a goal back when Conor Townsend flashed a ball across the face of goal, which Jordan Hugill almost connected with.
But another West Brom mistake nearly put the game beyond them – Clarke weakly played a free-kick midway inside his own half across the field, which was intercepted by Kebano who blasted low and wide after running into the box alone.
West Brom brought on Diangana and Callum Robinson to try and give a renewed impetus to their attack, but it was defender Bartley who again almost scored as he headed a 61st-minute corner wide before Jake Livermore put a Townsend cross over the bar from close range following good work by Diangana in the build-up.
The game was all but ended as a contest with 20 minutes to go following Furlong’s red card, which may be seen by some as controversial.
De Cordova-Reid’s superb through ball put Wilson clear, but Furlong’s studs appeared to make slight contact with the pass before the defender took down the former Liverpool midfielder and the defender was sent off for denying a goalscoring opportunity.
Adarabioyo should have scored with 10 minutes to go with a free header at the far post but Sam Johnstone was able to palm it clear before Mitrovic hammered in his third from a couple of yards out following some excellent footwork on the byeline from Wilson to set him up.
Adarabioyo’s red card shortly after was the only sour note for Marco Silva’s side as their hopes for a return to the Premier League were given a boost with victory over one of their biggest rivals.