Kriechmayr beat Mayer by 0.17 seconds on Garmisch-Partenkirchen's Kandahar piste, with Switzerland's Marco Odermatt third in the German resort.
The win, in warm conditions in the Bavarian Alps that favoured the early starters, was the second of the season in super-G for Kriechmayr, while Olympic champion Mayer has had six podiums in a row.
Kriechmayer, who also won in Kitzbuehel two weeks ago and started with bib number five on Saturday, extended his lead in the World Cup super-G standings with 341 points to Mayer's 240.
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The championships start in the Italian Dolomites resort on Monday with a women's Alpine combined. The men's and women's super-G races are on Tuesday.
"The world championships are always really unpredictable," said Kriechmayr. "Its own race, a new day, a new course, a new slope. I'm in really good shape, and I hope I can ski as fast as today."

Kriechmayr wins super-G in Garmisch to extend World Cup lead

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