Rast qualified on the front row alongside polesitter Wittmann and, once the safety car race start had cleared, the Audi driver hounded Wittmann through the opening corners and the pair ran side-by-side after the De Strubben hairpin.
A safety car caused by Daniel Juncadella moments later paused the battle, with Wittmann able to gradually pull away from Rast late on.
Rast and Wittmann agreed that the Audi driver's bid was helped by his manufacturer's ability to switch the cold tyres on quicker than the BMW, which tends to find tyre performance later in a stint.
The battle was decided when Rast's stablemate Nico Muller used a long-running opening stint to jump both Wittmann and Rast, with the BMW driver then able to pass Muller for victory when the Swiss driver struggled on cold tyres.
Rast said: "[In] my position as the leader, you cannot take crazy risks, Marco will agree to that. He knows it.
"I was trying to go past but for me, in the end, the points were more important than the victory and I didn't want to do stupid things, so I kept it on the Tarmac and tried to be safe.
"I tried to pass him, but there was no safe away around him. I stuck to the plan."
Marco Wittmann, BMW Team RMG, BMW M4 DTM, Nico Müller, Audi Sport Team Abt Sportsline, Audi RS 5 DTM, René Rast, Audi Sport Team Rosberg, Audi RS 5 DTM