Staal, 23, will join his older brother Eric on the Hurricanes.
"Jordan is an elite two-way player who possesses a rare combination of speed, size, scoring ability and defensive responsibility," Hurricanes general manager Jim Rutherford said in a statement. "For his young age, he has a wealth of NHL experience, including winning the Stanley Cup with Pittsburgh in 2009. And he is obviously a natural fit for our team in joining our captain, his older brother Eric."
Staal earns $4.5 million US next season, the final year of his current contract.
Sutter, 23, will fit for Pittsburgh in their No. 3 centre spot. He's played all 82 games the past two seasons for the Hurricanes, who selected him 11th overall in 2007.
He is the son of former NHL player and coach Brent Sutter.
Dumoulin, 20, is an American defenceman who played at Boston College.
The Pens used the eighth pick they obtained from Carolina to select WHL defenceman Derrick Pouliot.
Pittsburgh wasn't done, late in the evening trading defender Zbynek Michalek to Phoenix.
It is a return for the 29-year-old blue-liner, who spent five seasons with the Coyotes before signing as a free agent with Pittsburgh in 2010.
He has three years left on a contract that includes a cap hit of $4 million per season.
The Penguins receive 19-year-old defenceman Harrison Ruopp, minor league goalie Marc Cheverie and a third round pick in this draft.
Veterans Mike Ribeiro and Lubomir Visnovsky were also dealt by early in the first round Friday.
Ribeiro, 32, was sent from Dallas to Washington for Cody Eakin and a second round pick in this year's draft. The centre is in the final year of his contract in 2012-13, with a salary cap hit of $5 million.
The 32-year-old has 63 points last season, the eighth straight year he has recorded 50 or more points.
Forward Eakin split time between the Capitals and their American Hockey League affiliate.
Visnovsky, who'll be 37 when the next season starts, heads to the New York Islanders. The Anaheim Ducks receive a second round pick in 2013.
The defenceman has a cap hit of $5.6 million next season, the final year of his current deal.