Austrian Veith, skiing second, charged down the course in one minute 5.77 seconds, a time that none of the following skiers was able to get near.
Veith's last win was in the giant slalom at Meribel in March 2015, the year she won the overall World Cup title for the second time.
She missed the whole of the 2015-16 season after suffering a serious knee injury and only returned to racing one year ago.
Tina Weirather of Liechtenstein was second and Italian Sofia Goggia third.
"It's really very emotional and difficult to describe," Veith, close to tears, told Austrian broadcast ORF. "It's something I dreamed about during the most difficult times."
Vonn, who suffered a back injury which left her in enormous pain at St Moritz last week during another Super G race, said she wanted to concentrate her efforts on the Winter Olympics in Pyenongchang in February.
"Unfortunately I'm not racing today. Knee is a bit sore from yesterday so to be on the safe side I'm going to give my body some rest," she said on Twitter.
"My focus is on the Olympics so no need to risk anything now. Still going home very happy after my win yesterday."
Vonn's win in Saturday's Super G was her first since the downhill at Garmisch in January.
The finest woman skier of her generation, Vonn was downhill gold medallist at the Vancouver Winter Olympics in 2010 but missed the 2014 games in Sochi because of a knee injury.
The 33-year-old was also sidelined for 11 months after suffering a knee injury in Andorra in February, 2016 and broke her arm in training in Colorado the following November.
(Writing by Brian Homewood in Bern,; editing by Ed Osmond)
