Feuz, the winner of the last two downhills at Kitzbühel, was second through with Matthias Mayer of Austria – who would be on course for a fourth straight downhill podium – third.
The win for Paris was his 15th career World Cup victory in downhill, extending his lead among active skiers (Feuz is second on 12) and moving him to joint-fourth all-time. It was also his 19th win in all disciplines, setting him up for a big home World Championships.
The race was paused for 20 minutes by a high-speed crash for Germany's Josef Ferstl, who caught the edge of one of his skis on the Seilbahnstadlsprung jump and landed on his side.
He slid down into the safety netting and crashed into an air cushion, taking out a significant amount of netting with him.
Incredibly, Ferstl was unhurt and managed to stand up and untangle himself, receiving the all-clear from the race doctors as he managed to ski off the mountain on his own.
Coming off the back of a serious injury, Paris was in search of his first win since rupturing his ACL last January.
The fifth skier down the course, the Italian took an attacking line in the opening segment and found himself inside Feuz's time at the first two time splits.
Although Paris dropped some time in the middle, he was never more than a tenth outside of his Swiss rival's time and he was back ahead on the clock through the Hölle.
Paris continued to gain speed in the last third of the course and eventually crossed the line 0.37 seconds ahead of Feuz.
Feuz, who took his 39th career World Cup downhill podium which put him third all-time, earlier looked smooth and took nice, tight lines down the piste.
However, the Swiss will be disappointed losing time at the bottom of the course, finishing only three-hundredths faster than Mayer, who was first down the course.
The results keep Feuz and Mayer in first and second in the downhill Cup standings, while Paris overtakes Johan Clarey for third.
"I'm a little bit surprised, I pushed... it was a lot of fun today," Paris told FIS afterwards.
"It was, every day, a little bit better," he said of returning from injury. "I had more confidence on skis, but I know it takes a lot to be back on the podium and to get the victory. Training yesterday gave me a lot of confidence that I was skiing very solid, and today I was pushing very hard to the bottom. I'm very happy.
"I hope it's coming back a little bit more, my skiing."
The race in Garmisch, originally scheduled for Saturday, was brought forward a day and switched with the planned Super-G due to a poorer weather forecast for Saturday.
After the Super-G, the World Cup circuit will pause for the FIS Alpine World Ski Championships in Cortina d'Ampezzo, Italy, where Paris will now be one of the favourites to win.
However, Paris' compatriot Sofia Goggia, Italy's speed queen, will miss the championships after suffering a knee fracture sustained when she fell in Garmisch last weekend while returning to her hotel.