Vettel had led the majority of the race from pole position while Hamilton had to slice his way through the pack from 14th after losing hydraulic pressure during qualifying.
But when a rain shower exploded the race into life with 25 laps to go, the Brit ended up in the box seat on a set of fresh ultrasoft tyres, cutting Vettel’s lead from 24 seconds to 12 in just seven laps.
The Ferrari driver subsequently lost control at the Sachs Kurve and slammed into the barriers, triggering a safety car period during which Hamilton inherited the lead.
He went on to win the race and leapfrog Vettel in the F1 World Drivers’ Championship, which he now leads by 17 points.
And while Mercedes team boss Wolff was loathe to celebrate the demise of a rival, he reckons Hamilton had a direct effect on proceedings.
“Sebastian in the front knew that he needed to continue to drive fast in order to not compromise his race situation. That led to the mistake, I guess,” Wolff said.
“It was an error, but the feeling I have is that as much as we enjoy winning and we fight hard on-track and we are rivals, I can relate how that feels and it’s not nice.
“We need to find the right balance between attacking and keeping the lead and that’s coming from behind and in the same way keeping the car safe on track, and that is not always easy.
“Today that went against him.”
Former F1 world champion and fellow German Nico Rosberg disagreed, claiming Vettel was not under as much pressure as he thought.
“He had such an advantage, he could have taken out a bit more speed and just played it a bit safer,” Rosberg said.
“[He] just pushed too much and shunted it and shoved into the wall, on his own. That’s a tough one. I can really feel for him.
“I think he’s going to remember that as one of the darkest moments of his whole career, in front of his home crowd, with such a chance to get a huge points haul over Lewis.”