The four-time overall World Cup champion clocked the fastest time in the Dolomites to finish 0.12sec ahead of compatriot Julia Mancuso with Slovenian Tina Maze third at 0.18.
Vonn, 30, needs just one more win to equal the 62 World Cup wins set by Austrian Annemarie Moser-Proell between 1970 and 1980.
And the Italian resort will offer the American skier, who is back on strong form following a high speed crash in early 2013, three chances to do so.
Cortina will on Friday host last weekend's cancelled downhill from Bad Kleinkirchheim, Austria, along with a second downhill on Saturday and a Super-G on Sunday.
Vonn, who was out for 18 months with injury, has already won five times on the Olympia delle Tofane slope and last won in Italy in the 2013 downhill.
"It's a piste that I like a lot. I got my first podium here (3rd in the downhill, January 18th 2004) in the World Cup and I have a really good understanding of the hill," said Vonn.
Only a new injury can stop the American making history, although Moser-Proell's mark came during a time when the Super-G did not exist.
Maze, meanwhile, will be looking to extend her lead in the overall World Cup standings, as he sits 252 points ahead of American Mikaela Shiffrin.