Pärson acknowledged she had let a chance of a win slip - "my downhill wasn't totally error-free and I was a bit cautious in the slalom - I can slalom better than that."
Overall reigning champion Vonn closed to within 13 points of current overall World Cup leader Maria Riesch of Germany, who was disqualified after straddling a gate on the slalom run.
Vonn had given herself work to do by placing third in the downhill. She almost toppled over on the top half of the course before righting herself and pocketing a win which left her on 716 points to 729 points for Riesch.
Canada's surprise package Larisa Yurkiw was fastest on the downhill but fell away as Vonn went on to win in an overall 2minutes 40.53 seconds with Zettel 0.3seconds and Pärson 0.66 seconds adrift.
Pärson, who had won the previous super-combined at St. Moritz saw Yurkiw, just 20, steal her downhill thunder and ultimately had to settle for her podium placing.
Yurkiw thereafter missed a gate to see her early challenge fall away.
Zettel's showing moved her up one place in the overall standings to third.
"I'm a bit surprised to have won here today - especially after making a mistake and almost falling at the first jump in the downhill," Vonn admitted.
"I didn't risk things too much in the slalom as I didn't think I was going to win and I absolutely wanted to finish so I wouldn't lose too many points.
"I am sorry for Maria - I know how she feels," said Vonn, who added she was now full of confidence for Sunday's downhill - as long as the Hot Air jump does not come close to tripping her up once again.
Zettel said she was delighted to have run Vonn so close on the day.
"I am very satisfied with my result and astounded at my good tenth place in the downhill. It's a shame I made a small error in the slalom. Despite my downhill result I won't do Sunday's as I want to concentrate on Cortina," she added.