Stolz finished third in the second of the two races at the Dutch venue on Sunday, holding off two-time champion Wittmann by just 0.249s in a tense battle.
The AMG works driver was running behind Wittmann in the first stint but jumped his fellow German by pitting a lap later. Stolz's HRT crew serviced his Mercedes-AMG GT3 in 7.9s compared to the 9.3s it took for DTM newcomer Project 1 to change all four tyres on Wittmann’s M4 GT3.
The 27-year-old, who broke his DTM duck at the Nurburgring last season, then had to fend off the double series champion who kept the pressure up until the chequered flag.
Speaking after his first podium result since last year’s Red Bull Ring event, Stolz said he had to rely on Mercedes’ superior traction out of the corners to keep Wittmann at bay on Zandvoort’s straights.
“In the early stages when he had a lot of traction then it's always hard to fight the BMW because feeling-wise they are 100km/h quicker,” he said.
“But as soon as he lost a little bit of the tyre, I saw that I was better on traction and I could always place myself well.
“Then it was quite easy to defend because in the last laps I saw if I do no mistakes then he will stay behind.”
Wittmann also felt Stolz had an advantage exiting low-speed corners, which meant he was unable to pull off a move and score his first podium of the season.
“He had extremely strong traction out of the slow corners and accordingly always had a gap for the straights,” Wittmann told broadcaster ran.de. “That's why there was no way past him.
“We had phases in the race when I was faster and caught up with him, then he was faster again. It was a constant change. We had a pretty similar pace.
“My hope was that maybe toward the end of the race his tires would go down. But in the end, there was nothing we could do.”
Stolz endured a tough start to the season at Oschersleben along with the rest of the Mercedes contingent, ending up 25th and 23rd in the two qualifying sessions before retiring from both races.
Asked if he felt relieved to score a podium with a new chassis after his Oschersleben struggles, Stolz said: “Yeah, definitely, good day at the beach.
“We saw already from Friday on that we are much better than in Oschersleben. We basically had a new car, because we had a broken chassis in Oschersleben, so it's great to come back like this.
”We saw already on Saturday we made some good steps in the right direction and I feel on Sunday we maximised some stuff.”
Additional reporting by Heiko Stritzke