The 24-year-old - already a winner in La Molina and Semmering - timed 1 minute 58.96 seconds beat home Nicole Gius of Italy by 44 hundredths of a second while Slovakian Sarka Zahrobska was third 63 hundredths adrift.
Riesch, who was recording her ninth career victory and fourth in the slalom, extended her lead in the slalom standings after five races. She replaced Vonn at the top of the overall standings after the American fell on the second run, having recorded the best time on the first leg and was well ahead at the intermediate times on the second.
Riesch and Vonn are great friends - they spent Christmas together at the former's home - and the German admitted that it was tough competing against her.
"Today (Sunday) was a little difficult," said Riesch. "I won and I was really happy, she (Vonn) went out and was really unhappy."
Riesch, though, added that even after three successive wins she didn't necessarily have the title in the bag.
"It's great but there are still a lot of races... things change quickly, three weeks ago, I was more than 200 points behind Lindsey," said Riesch, who had a 77-point lead over Vonn.
Earlier, Nicole Hosp of Austria, the 2007 World Cup champion, injured her knee when she fell preparing for the race. Hosp, 25 and standing sixth this season ahead of Sunday's contest, went down and stayed down on the Sljeme piste and organisers said she was taken to
hospital before being transferred to Austria for an IRM scan.
Hosp suffered a similar misfortune in December at Aspen in the giant slalom.