Having trailed Petra Vlhova after the first run, Shiffrin took the lead on the second and finished 0.75 seconds ahead of her rival in Killington, Vermont, moving level with the record that Stenmark has held for 32 years.
“I actually didn’t know (about) the record,” Shiffrin told NBC Sports.
“I won’t say it’s not meaningful. It certainly is, but I’m trying not to focus on those numbers. The closer I get to these marks, it’s hard not to think about it and want that.”
Stenmark, the Swedish slalom specialist who competed in the 1970s and 80s, also holds the record for the most World Cup wins with 86, while Shiffrin is third on the all-time list with 71.
Vlhova led Sunday’s competition with a time of 49.87 seconds on her first run, 0.2 seconds ahead of Shiffrin.
But an error early on the second run cost the Slovakian and enabled Shiffrin to take the victory — her fifth consecutive slalom win in Killington.
Switzerland’s Wendy Holdener was third, 0.83 seconds behind Shiffrin.
The result means Shiffrin, a two-time Olympic gold medalist, leads the overall World Cup standings on 360 points after five events, 20 ahead of Vlhova.
“At my top speed, this (the second) run, I don’t know if I can ski faster slalom than that,” she said.
The women’s World Cup now moves to Lake Louise, Canada, with the downhill taking place on December 3.