The American is in unstoppable form, winning a slalom on the same piste on Saturday after celebrating two giant slalom victories on Italian snow in Kronplatz on Tuesday and Wednesday.
Stenmark won his 86 races in the 1970s and 1980s, with the first in a slalom at the Italian resort of Madonna di Campiglio in December 1974 and the final victory in a giant slalom at Aspen in 1989.
Regarded as the greatest slalom skier, all of his wins were in slalom (40) or giant slalom (46).
Shiffrin has triumphed across the speed and technical disciplines with 52 wins in slalom, 19 in giant slalom, five super-G, three downhills, five in parallel and one in the combined.
"I'm a little tired today, I wasn't sure if I could hold it over the whole course," said Shiffrin.
"I'm just trying to focus about the simple things, thinking about the skiing ... there's so much that can still happen, I'm not really focused on the record even though yesterday evening I did have some time to think about it."
Shiffrin made her World Cup debut in a giant slalom in Spindleruv Mlyn in 2011 as a 15-year-old.
The American has won five of eight slaloms so far this season and 11 World Cup races, making it her best campaign since 2018-19 when she won a record 17 times.