The teammates outpowered a 48-strong pack in the uphill sprint in Barcelona's Montjuich park, where the sixth stage of the Tour de France finished last year.
Joaquim Rodriguez of Spain was third and kept the race lead.
"It was the same finish as the Tour but the very different final approach route today meant I could go for the win," the 29-year-old Dumoulin told reporters.
"We dropped the top sprinters because it was a tough finale, but as I'm a small guy I could handle the climbs better and then use my power to take the sprint.
"Getting first and second on the stage was more circumstantial than planned. Rein's lying third overall so we wanted to keep control of his rivals by staying close to the front and then with 200 meters to go I decided to go for it." Cofidis announced on Friday that they were extending their sponsorship of the team until the end of 2012.
"This is our twelfth victory of the season but after yesterday's news this one's very special," team manager Eric Bouyer told Reuters.
"We told the sponsor that the best way of thanking them was with a win this weekend, and we've got the top two places in Catalunya's hardest race." With one easy stage of the event remaining, Rodriguez is poised to become the first Catalan rider to win his home race in 27 years.
"It's not over yet but the end's in sight," Rodriguez told reporters. "That's a good feeling."
