The Cottagers withstood Millwall's best efforts in the first half before showing their class after the break to put the pressure back on the Bluebirds in the quest to follow Wolverhampton Wanderers to the Premier League.
The hosts continued their early crossing assault and were perhaps unfortunate to have a goal disallowed on 14 minutes, when Jed Wallace was penalised for climbing on Matt Targett before George Saville swept home the ball from close range.
Fulham boasted their own aerial target in Mitrovic, and the on-loan Newcastle United striker got above Shaun Hutchinson from a Targett cross but could not direct his 22nd-minute header on target.
Millwall's prowess from crosses forced Marcus Bettinelli to try to take charge of his box, but one flap from the Fulham goalkeeper fell kindly to Wallace and he had to be bailed out by Tim Ream's last-ditch clearance off the line.
The full-backs were a useful attacking outlet for Fulham and Targett came close to breaking the deadlock in first-half stoppage time when he rattled the crossbar from 25 yards after being teed up by Tom Cairney.
Fulham raised their game significantly in the second period and took the lead within a minute of the restart, as newly-crowned Championship Player of the Season Sessegnon slotted through the legs of Jordan Archer, after he had parried a shot on the turn from Mitrovic, for a 15th goal of the season.
McDonald has been an unsung hero for the Cottagers all season but he had his moment in a high-stakes London derby as he skilfully skipped past Saville in midfield and bent a long-range shot beyond Archer.
Millwall could not recapture the attacking threat that they showed in the first half and were in frequent danger of falling further behind, with Sessegnon working Archer and going within a whisker of the bottom corner with a pair of left-footed drives.
However it was the weaker right foot of Mitrovic which put the nail in the Millwall coffin as he thrashed a shot into the top corner on 89 minutes, after substitute Tomas Kalas had skipped out from defence with the ball.
Their biggest home defeat of the season might not be a nail in the coffin of Millwall's playoff hopes though, as they hang onto sixth place heading into the weekend, albeit with a group of five teams chasing them down.
Meanwhile Fulham are now two points above Cardiff, although the Welsh outfit do have two games in hand.
MILLWALL (4-4-2): Archer; Romeo (O'Brien, 87'), Hutchinson, Cooper, Meredith (Cahill, 77'); Marshall (Elliott, 65'), Williams, Saville, Wallace; Gregory, Morison
FULHAM (4-3-3): Bettinelli; Fredericks (Christie, 90'), Odoi, Ream, Targett; McDonald, Johansen, Cairney; Piazon (Kalas, 83'), Mitrovic, Sessegnon