The Serbia striker, 25, took his tally to 11 goals in 13 games this term with his treble at Craven Cottage.
The former Newcastle man also has five international goals this season and has scored eight in his last five games for club and country.
Ivan Cavaleiro then fired at Hatters keeper James Shea, although Tim Ream's error at the back allowed Izzy Brown to set up Luton's first opportunity, which James Collins thumped wide from a tight angle.
Mitrovic showed how it should be done as Fulham took a 16th-minute lead. Cavaleiro provided the pass that allowed the Serbian to swivel and lash high beyond Shea from the edge of the box.
Shea was soon back in action, diving to keep out drives by Knockaert and then Mitrovic, whose bicycle kick moments later was too high.
Luton needed a response, but another Brown-Collins combination saw the latter again blast goalwards but fail to hit the target.
Knockaert continued his shoot-on-sight policy at the other end but he was too high on this occasion, while Collins' next effort struck a defender.
The score remained 1-0 at the break after Cavaleiro curled a right-footer just wide and Mitrovic, on the slide at the back post, could not convert at full stretch.
Luton came out with intent, Harry Cornick finding the side-netting after Brown set him up.
Brown had a go himself and won a corner, but it was not long before Mitrovic doubled the lead in the 53rd minute.
Bobby Reid's low ball across the box from the right only needed a connection and Mitrovic was there ahead of the centre-backs to convert from four yards.
Luton pulled one back on the hour mark through Potts, who lost his marker to head home Brown's free-kick.
Fulham's response was a free-kick move in the 67th minute that saw Mitrovic claim the match ball.
Knockaert played it to Joe Bryan on the left and Mitrovic stooped to nod his delivery into the box beyond Shea.
Collins came close to his 50th league goal for Luton, but Shea then was required to divert Cavaleiro's drive at the other end for a corner.
LuaLua pulled another back for Luton in stoppage time when fellow substitute Luke Bolton's ball across the box reached him at the back post, but it was not enough to deny Fulham the three points.