The striker produced three clinical finishes - although Swansea claimed Mitrovic benefited from a generous offside decision for the opening goal - as Marco Silva's side clinched their second win in five league games.
Jamie Paterson replied for the visitors after Mitrovic had put the home side two up, but they were unable to work their way back into the game and suffered a first defeat in five league games.
Silva's side started positively with Harry Wilson immediately causing problems for the Swansea backline.
A through ball from Joe Bryan sent the former Liverpool midfielder into the Swansea penalty area where he went to ground under a challenge from Ryan Manning but Wilson's appeals for a penalty were ignored.
If Fulham were frustrated on that occasion, they benefited from referee Joshua Smith's next major decision when Mitrovic put them ahead in the 12th minute.
After Swansea had failed to clear their lines, Tim Ream headed the ball back into the Swansea area where Mitrovic was standing unmarked on the edge of the six-yard area.
The forward turned and shot past keeper Ben Hamer and the match official awarded the goal despite Swansea protests that Mitrovic was in an offside position.
The momentum was with Fulham but Mitrovic and Bobby De Cordova-Reid both failed to make the most of good chances to double the lead.
They did not have to wait long, however, before Mitrovic added his second in the 32nd minute after Fulham took full advantage when Cottagers left-back Joe Bryan intercepted a misplaced pass by Swansea defender Ben Cabango.
Silva's side pressed forward quickly down the left and Mitrovic was on hand to meet Neeskens Kebano's low cross and direct his first time finish inside the far post.
Swansea had not threatened but they forced their way back into the game in the 38th minute when Jamie Paterson collected Joel Piroe's pass and finished well past keeper Paulo Gazzaniga.
But Fulham responded to the setback positively and restored their two-goal lead when Mitrovic completed his hat-trick in the 45th minute with another first-time finish, this time after meeting Denis Odoi's low cross from the right.
Swansea appeared to have little hope pf clawing their way back into the game but they responded well at the start of the second half with Flynn Downes failing to make most of a good shooting opportunity and Ethan Laird directing a deflected shot against the woodwork.
But Fulham regained control and saw out the game comfortably.