Dversnes, an Uno-X Mobility rider, joined Martin Marcellusi, Mattia Bais and Mirco Maestri in the break and prevailed in a four-man sprint to the finish line.
Italians Maestri and Marcellusi also made the podium, in second and third place respectively.
"This was my big shot," Dversnes said. "You always think about (the win) on the way, but when we had two minutes' lead pretty late in the race, you of course start believing."
Safety concerns
The breakaway group set a high pace in the flat stage, maintaining an average speed of over 51km per hour.
The peloton hung back in the 157km ride from Voghera as they entered Milan for four laps in a 16.3km local circuit with the leaders still over two minutes ahead.
However, several riders faced trouble with the placement of barriers near the narrow finish line, and some approached race director Marco Velo's car to complain about them, including leader Vingegaard.
"It's dangerous," the two-time Tour de France winner was heard on the broadcast telling Velo through the car window, just as his bike shook hard as he rode over a pothole.
"Look, I almost crashed now," Vingegaard shouted to the director, pointing out an additional issue with the rough surface.
Soon after, the race jury ruled that the final five kilometres of the stage would not count for general classification.
Later, that was extended to the entire final lap for the pink jersey, with the organisers announcing the time for general classification would be recorded with one lap still to go. Only the stage win and points would still be in play in the final lap.
The four leaders were 52 seconds ahead of the peloton going into the last lap, and despite a late chase from the sprinters, they kept a narrow lead.
Dversnes, 29, outpaced the exhausted Italians in the final yards and collapsed on the ground after finishing the stage in three hours, three minutes and 18 seconds.
Vingegaard safely crossed the line with the peloton, retaining his overall lead of two minutes and 26 seconds ahead of second-placed Afonso Eulalio.
The race continues on Tuesday in Switzerland, with a 113km ride through the mountains from Bellinzona to Cari.