Rooney converted after Tim Ream had handled early in the second half but Mitrovic expertly dispatched his 22nd league goal of the season to earn Fulham a point.
Both sides could have won it in the closing minutes, with Fulham goalkeeper Marek Rodak making two superb saves as Rooney drove Derby forward.
It was a special night for the former Everton and Manchester United forward, who played in a more attacking role in the absence of the injured Duane Holmes and had a big influence on the game.
Derby started well, forcing an early corner which was worked to Tom Lawrence just outside the box but his shot cleared the stadium roof.
His next effort was deflected behind and, when Rooney's corner was cleared, the former England skipper found Lawrence again but his shot lacked the power to trouble Rodak.
Fulham were having periods of possession but Derby were more threatening and it needed a smart save from Rodak when Rooney found Matt Clarke at the back post with a free kick in the 23rd minute.
The visitors twice went close in the 29th minute when Mitrovic just failed to connect with a cross and, when the ball was played back in, he headed straight at Ben Hamer.
Derby threatened once more in the 36th minute when Anthony Knockaert was caught in possession and Lawrence's low shot from the edge of the area was superbly turned behind by Rodak.
The home side went ahead in the 55th minute when Fulham played themselves into trouble and Tim Ream used a hand to stop Martyn Waghorn going through.
Rooney stepped up and coolly chipped a Panenka penalty into the net as Rodak dived the wrong way.
Fulham had lacked urgency and it was no surprise when they made a double change in the 65th minute, which paid off six minutes later.
Bobby Decordova-Reid had a shot deflected behind and Cavaleiro fired over before Derby came close to regaining the lead in the 85th minute.