Beat Feuz of Switzerland, the favourite for the overall World Cup trophy, crashed and did not finish the race, boosting the chances of Austria's Marcel Hirscher to overtake him at the weekend.
Innerhofer finished in a time of 1min 21.24sec in his first super-G victory since he won the World Championship in the discipline in Garmisch-Partenkirchen, Germany last year.
France's Alexis Pinturault came second in 1:21.26, with Hirscher grabbing a crucial third place and his first ever super-G World Cup podium, a further 0.04 seconds behind.
The 23-year-old Austrian thus stayed in the race for the overall crystal globe, advancing to 1,255 points, behind Feuz's 1,330.
Svindal finished 16th but this was enough to take his third super-G crystal globe ahead of Switzerland's Didier Cuche, who is retiring.
"I was lucky. I'm very happy," Svindal admitted after the race.
The 37-year-old Swiss veteran, who was ninth, missed out on his second crystal globe in two days, after crashing in the downhill on Wednesday.
He bid farewell to the competition in the arrival area by doing his trademark ski flip and bowing to the crowd.
Hirscher, who rarely runs the super-G, said ahead of Thursday's race that it was "an opportunity that should not be missed."
"I'm really glad it paid off," he said after finishing third.
"This is the best super-G result of my career. It's a great finals already, whatever happens."
Feuz insisted his fall had nothing to do with pressure to win the overall trophy, which he could have secured with a win on Thursday.
"Today I knew I just had to have a good run... I actually felt better than yesterday. I'm disappointed of course but... it happens."
Looking ahead, he favoured Hirscher to win even more points in his specialties, the slalom and giant slalom, over the weekend.
"I'll try to get a few more points but it's all very open," said the 25-year-old Swiss.