Fulham secure thrilling first win of the season
Mitrovic fired Fulham to promotion from the Championship with 12 goals on loan from Newcastle last term.
Now playing for Fulham on a permanent basis, he is doing all he can to ensure their stay in the top-flight is not a short one.
Jeff Hendrick had cancelled out a stunning goal from Ivory Coast midfielder Jean Michael Seri when Mitrovic struck with two headers in two minutes.
James Tarkowski pulled one back for Burnley, but Andre Schurrle's late strike ensured Fulham got off the mark after losing their first two matches against Crystal Palace and Tottenham.
Just three minutes had elapsed when Seri came up with a memorable first goal in English football.
Collecting a ball inside from Luciano Vietto 25 yards out, Seri turned, looked up and launched a ferocious shot which left Clarets goalkeeper Joe Hart grasping at thin air.
Yet if Burnley were feeling the effects of their midweek trip to Greece it was not immediately apparent, as they took just seven minutes to equalise.
A loose pass from Maxime Le Marchand in midfield allowed them to break with Aaron Lennon leading the charge.
The winger raced to the edge of the area before squaring the ball to Hendrick, who needed a couple of bites at the cherry before beating Fulham keeper Marcus Bettinelli at the far post
However, when Hart misjudged Tom Cairney's deep cross Mitrovic stole in at the far post to head Fulham back into the lead.
Moments later Mitrovic struck again, this time with a glancing header.
Shellshocked Burnley did manage to get back into it four minutes before half-time, although there was a hint of offside as Tarkowski prodded in Ben Mee's header from a corner.
They could not muster a response after the break, though, and Fulham wrapped up the victory seven minutes from full-time.
Mitrovic was denied a hat-trick when Hart pushed his shot against a post but Borussia Dortmund loanee Schurrle drilled in the rebound.