The HRT driver enjoyed a perfect rolling start from pole position as his rivals tiptoed through the tight, technical opening sequence of corners.
Ten minutes later came a brief safety car intervention to clear debris. This destroyed the clear lead Stolz had already built up, but the German simply pulled away again.
He then pitted at the first opportunity when the window opened, despite this meaning a long second stint that would ask much of the tyres on a hot day.
The move ensured him track position over Thomas Preining, and he was able to manage a comfortable lead to the end and claim his second career DTM win.
Preining had run third behind Ayhancan Guven before the pitstops, but pitting one lap earlier and good work from his Manthey EMA crew vaulted him past the Turkish driver and into a runner-up position he would also hold to the end.
Guven kept Preining within sight to complete the podium, ahead of the battling ABT Audis of Ricardo Feller and Kelvin van der Linde.
Lamborghini star Mirko Bortolotti, who led the points battle coming into this weekend, had a rough day out at the twisty little Sachsenring track and lost the lead of the championship to Preining.
The Italian ran fourth before the pitstops, but then it all unravelled. His troubles began with an ABS problem that led to the rear wheels spinning while the car was jacked up during his pit visit.
Officials took a dim view and Bortolotti was immediately issued a slow-lap penalty. On top of all that, the SSR Performance driver had to contend with flat spots on his front tyres after a big lock-up exiting the pits.
Bortolotti had to settle for ninth place and will go into Sunday’s second race with a six-point deficit to Preining.