Dumoulin led the chasing pack across the line, five seconds back, to replace Germany's Marcel Kittel as the overall leader.
Sprinter Kittel, winner of the previous two stages before Monday's rest day, struggled on the climbs in the second half of the day's stage.
"It's a really nice feeling," Ulissi, who has now won five Giro stages throughout his career, said.
"When I was small I dreamt about things like this, it's a beautiful emotion."
Dumoulin (Giant-Alpecin) leads the overall standings by 20 seconds from Bob Jungels (Etixx-Quick Step) going into Wednesday's stage to Benevento.
(Reporting by Martyn Herman; Editing by Toby Davis)
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