Hill took the lead on the 27th lap as leader Schumacher, shown the black flag five laps earlier, finally pulled into the pits for a five-second penalty imposed for passing on the warmup lap before the start of Sunday's race.
Schumacher was later fined $25,000 and his team reprimanded for ignoring the black flag.
"I'm real unhappy about this," a stern-faced Schumacher said. "It's nothing I want to talk about."
The controversy began when Schumacher, second on the grid, passed pole-sitter Hill before the first turn of the first warmup lap, a violation of Formula One rules.
Schumacher's team was informed of the infringement and the driver was given the black flag on the 22nd lap, but he drove past it repeatedly while race director Roland Bruynseraede went to the Benetton pit area to explain.
Hill, who had been trailing by two seconds before the German was pulled, built a huge advantage as Schumacher's Benetton Ford spent 35.5 seconds in the pits -- the penalty plus braking and accelerating time.
Schumacher, who then had to deal with gearbox problems, was unable to make up the deficit and Hill beat him home by 18.778 seconds in his Williams Renault. The winning time was one hour, 30 minutes, 3.640 seconds.
"I think this is the best day of my life," said Hill, winning for the first time the race that his two-time world champion father Graham Hill never won. "It's like a dream. I feel this has completed the hole that my father left in his record and I'm sure that he'd be delighted."
Schumacher later appeared to blame his warmup-lap error on Hill.
"He was going a bit slow in the corner," Schumacher said, "and we were all pushing quite hard and I just didn't want to brake so hard and maybe lock up my tires."
Frenchman Jean Alesi took third place in a Ferrari.
Fifth-place Mika Hakkinen, trying to pass Rubens Barrichello on the final turn of the race, collided with the Brazilian. Both cars were crippled, although both finished.
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