Paris trailed Innerhofer on the upper section of the icy course but was faster at the bottom and finished 0.36 seconds ahead of his teammate.
Beat Feuz, the Swiss racer who won the season-long World Cup downhill title last season, finished third, 0.52 behind.
Paris, who also won this race in 2012 and 2017, matched the record of three victories on the Stelvio held by Austrian greats Hermann Maier and Michael Walchhofer.
It was the 10th win of Paris’ World Cup career and his 25th podium result.
Paris’ speed was clocked at nearly 135 kph (84 mph) on the Stelvio’s only straightaway. Otherwise, he was letting his massive thighs absorb the bumps and terrain on the course’s constant turns.
“I wouldn’t say it was a perfect race but in the second part I let the skis run and gave my all, especially on the bottom, using all of my strength,” Paris said. “I always dream of winnning but especially when it’s really challenging. Then it really means a lot to me.”
Innerhofer has also had plenty of success on the Stelvio. He claimed the first of his six World Cup wins on this course in 2008 and was third in 2010.
Innerhofer put down the best early run with the No. 2 bib, despite pointing his ski tips a bit too high off the final jump.
Paris then came down five racers later and trailed Innerhofer at the first three checkpoints before gaining time back on the bottom.
While many skiers bent over in exhaustion at the finish, Paris began celebrating as soon as he crossed the line, pumping his fists and then raising his ski over his head once he came to a stop.
“Have you seen Dominik’s quadriceps? They’re 10 centimeters bigger than mine so I’m not surprised he wasn’t as tired as I was,” Innerhofer said.
Bryce Bennett of the United States finished fourth, 0.67 behind, to match his career-best result set in the Val Gardena downhill two weeks ago.
The surprise of the day came from Matthieu Bailet of France, who finished sixth with the No. 47 bib.
Feuz moved atop the discipline standings, 38 points ahead of Max Franz of Austria, who finished 12th.
Norwegian standout Kjetil Jansrud went off course on the upper section and abandoned his run.
Several skiers struggled with fatigue toward the end of the bumpy course.
Johannes Kroell of Austria lost control before the final jump and fell through the finish area. Kroell got right up and raised an arm to signal he was not injured.
Visibly exhausted after he crossed the line, Jared Goldberg of the United States let himself slide through the finish area. He finished 28th.
Ryan Cochran-Siegle, the American who was among the fastest in the training sessions, walked out of his ski on the top section and failed to finish.
Travis Ganong, another American skier, sat out after crashing in training a day earlier.
A super-G is scheduled for the Stelvio on Saturday.
More AP sports: https://apnews.com/apf-sports and https://twitter.com/AP_Sports