A thrilling scrap for second followed on lap 2 between Red Bull protege Lawson, who had cleared Sheldon van der Linde’s BMW on the opening tour.
Muller initially passed Lawson’s Red Bull-branded Ferrari going into the first chicane but a poor exit brought the AF Corse driver back into play, the two going side by side through Curve Grande.
Lawson had the inside line going into the second chicane but Muller didn’t give up, running over the kerbs to emerge out of the corner alongside the Kiwi.
However, all of this brought van der Linde into the picture, the Rowe Racing driver passing both of them in one bold move going into the first Lesmo to take second.
From there on, Lawson’s 55kg weight penalty – a combination of BoP changes and his victory on Saturday – became evident and he lost the final spot on the podium to Muller before falling into the clutches of T3 Motorsport’s Esteban Muth.
Eager not to concede the position, Lawson defended his line at the second chicane, only for the slightest of contacts between the pair to spin him around and leave him facing the wrong direction.
Meanwhile, the action happening for positions second-to-fourth allowed Kelvin van der Linde to extend his advantage out front, the Audi ace pulling away by five seconds by end of lap 7.
A late pitstop brought the gap down to four seconds but the Nurburgring 24 Hours winner was never challenged at the front, eventually crossing the line with 3.3s in hand to take a maiden DTM victory on his 25th birthday.
It was last year’s runner-up Muller who finished second in the Team Rosberg Audi, having got the jump on Sheldon van der Linde’s BMW with an undercut.
Lucas Auer’s decision to stop as soon as the pitlane opened at the end of lap 5 also paid dividends, the Winward Mercedes driver taking the final spot on the podium having started seventh.
The younger of the van der Linde brothers lost places to both Muller and Auer in the pits with a relatively late stop on lap 9, but was able to fend off the Walkenhorst BMW of two-time DTM champion Marco Wittmann in the closing stages to salvage fourth.
After qualifying 12th on the grid, Red Bull’s Alex Albon was able to move up the order in AF Corse-run Ferrari, finishing just 0.5s behind Philip Ellis’ Winward Mercedes in seventh.
2013 champion Mike Rockenfeller was involved in a long duel with Muth’s Lamborghini after having scythed his way from 17th on the grid, taking to the kerbs at the second Lesmo to finally complete the move.
The top 10 was completed by HRT driver Maximilian Gotz – who finished on the podium in Race 1 – ahead of Mercedes compatriots Vincent Abril, Daniel Juncadella and Maximilian Buhk.
Lawson rejoined the field last following his coming-together with Muth on lap 3 and could only recover to 14th at the flag, 32s behind race winner van der Linde.