Swiss rider Reusser (Movistar) finished the 21-km ride from Gevrey-Chambertin to Dijon in 27 minutes and 30 seconds, taking a 14-second lead over former champion Demi Vollering of the Netherlands in the general classification.
Vollering finished third on the day behind compatriot Lieke Nooijen, who was four seconds slower than Reusser.
Norwegian Haugset (Uno-X Mobility), who had taken the yellow jersey with a spectacular solo victory on Monday, was more than three minutes slower than Reusser and dropped to fourth in the overall tally, behind third-placed Cedrine Kerbaol of France.
"I’m super, super happy ... it’s the first Tour de France that I really saw as my goal of the year that I really targeted," said 34-year-old Reusser.
As Visma-Lease a Bike rider Nooijen threw down the gauntlet by clocking 27:34, Reusser started fast, crossing the intermediate point 20 seconds earlier than Nooijen.
It came down to the wire as Reusser pushed through the final km and managed to finish four seconds faster.
Vollering (FDJ United-Suez), who was already under way, made a frantic push in the final km but ended up 18 seconds slower than Reusser.
Haugset appeared to be struggling with exhaustion as she failed to capitalise on her two-minute cushion in the overall rankings.
The race continues on Wednesday with a 140-km hilly ride from Macon to Belleville-en-Beaujolais.