The Serb striker - who scored twice against Liverpool last weekend - was denied by home goalkeeper Jose Sa with 10 minutes left after Rayan Ait-Nouri had brought down Bobby Decordova-Reid.
Bruno Lage's Wolves, beaten 2-1 at Leeds on the opening day, have now not won in nine Premier League matches, with their last top-flight victory on 2 April.
Yet they started brightly against newly promoted Fulham, and Pedro Neto and Hwang Hee-chan saw almost identical chances on the left-hand side - supplied by the lively Daniel Podence - saved by Fulham keeper Marek Rodak.
The Cottagers almost gifted the home team a goal a few moments later following a mix-up in defence between Rodak and Tosin Adarabioyo, but neither Neto nor Podence could capitalise on the mistake.
Mitrovic had been quiet for most of the game and his only chance of note prior to the penalty was a ballooned shot into the stands during the first 45 minutes.
The frustration following his weak spot-kick, however, boiled over as a challenge on Morgan Gibson-White led to the pair squaring up to each other and both receiving a booking in added time.