The Cottagers could have secured their spot on Good Friday but a 2-1 defeat at Derby was the first time they had suffered successive defeats this season.
However, they bounced back at Craven Cottage and took the lead with their first real chance of the game as Mitrovic slotted home.
Carvalho added Fulham’s second and just before half-time Mitrovic made it 40 Sky Bet Championship goals when he took a touch and fired the ball past the Preston goalkeeper.
The Serbian forward had already cruised past Ivan Toney’s Championship scoring record with 14 games remaining in the season and now sits just two behind Guy Whittingham’s 42-goal haul from a 46-game second-tier season for Portsmouth in 1992-93.
Fulham have been dominant in the second tier this season and secured promotion with 26 wins, eight draws and just eight losses, having scored 98 goals.
Preston came close to taking the lead in the fifth minute when Cameron Archer ran down the left before playing in Ched Evans, whose shot rebounded off Tosin Adarabioyo and the home side were able to scramble the ball away.
Goalkeeper Marek Rodak had to be alert again two minutes later to tip Ben Whiteman’s effort over the crossbar and keep the score level.
Fulham scored from their first real attack of the game, with Joe Bryan coming inside from the left and cleverly playing in Mitrovic behind the Preston backline for the Serbian to slot home through the legs of Daniel Iversen.
The Cottagers had a chance to add to their lead in the 24th minute when the ball came in from Neeskens Kebano to Mitrovic and he backheeled the ball to Carvalho but his shot was wide of the target.
The home side doubled their advantage just after the half-hour mark when Kebano’s ball into the box took a fortunate deflection into the path of Carvalho and he fired a first-time shot into the back of the net.
Fulham added a third just before half-time, with Mitrovic scoring his 40th of the season in clinical fashion, taking a touch and firing home after being played in by Harry Wilson, who tops the Championship’s assist charts.
Mitrovic came agonisingly close to his hat-trick less than five minutes into the second half when he pounced on a loose ball and ran through on goal, only for Iversen’s outstretched leg to divert the ball onto the crossbar.
Iversen then denied the 27-year-old again in the 53rd minute as Fulham continued to press for a fourth goal, but they lacked the same intensity as the first half and the scoreline remained 3-0, with jubilant fans pouring onto the pitch at the final whistle with their Premier League place confirmed.