The win is Mostert’s first since 2015.
Jamie Whincup also briefly led before he too suffered a flat tyre while on for a second placing, the third of the race after Tim Blanchard also lost a tyre.
Coulthard got the jump when the green flag flew to start the race and established a one-second lead in the opening lap.
Pole-sitter Whincup managed to file into second despite big pressure from behind, while there was another melee at the back which saw James Moffat spin and Scott McLaughlin pick up steering damage.
Mostert was applying pressure to Shane van Gisbergen and the Supercheap Auto Racing Falcon got underneath at Ascari to take third on the opening lap.
Coulthard was stretching his lead when the Shell V-Power Falcon picked up a left-front puncture on Lap 7, handing the ascendancy to Whincup.
Mostert, however, took the lead before the lap was out and began to run away with proceedings.
Whincup looked set to at least finish runner-up before the Red Bull HRT Commodore lost a left-rear tyre on Lap 11.
That left his team-mate van Gisbergen, who had staved off pressure from Tim Slade earlier in the race, in second, and he eventually crossed the line 9.7s adrift of car #55.
Slade did take third in the Freightliner Commodore, ahead of the Nissans of Todd Kelly and Michael Caruso, and the HSV Commodores of James Courtney and Scott Pye.
Will Davison, Jason Bright, and David Reynolds made up the top 10.
Garth Tander made 11th despite being the man who McLaughlin clashed with at the first corner, while Craig Lowndes came from the very rear of the 24-car field to finish 14th.
McLaughlin was eventually 17th in car #17, Whincup 19th, and Coulthard 20th.