Jake DeBrusk gave Boston a 2-1 lead at 4:43 of the third period when he put in a loose puck in front.
"Tonight [DeBrusk] should [feel good about his game]," Cassidy said. "He did a good job of simply playing behind [Dallas' defense], winning the foot race, creating that second effort play to create a turnover, and then the puck ends up on his stick in the slot."
Marchand scored into an empty net at 18:23 for the 3-1 final.
NOTES: Swayman became the first rookie goalie to start a season opener for Boston since Blaine Lacher on Jan. 22, 1995, against the New York Islanders. It was Swayman's 11th NHL regular-season game. … Marchand has scored seven goals in Bruins openers, the fourth-most in their history behind Cam Neely (12), Ray Bourque (nine), and Phil Esposito (eight). … Defenseman Derek Forbort (one shot) and forward Tomas Nosek (two shots, two hits) each made his Bruins debut. … The other players to score a team's first goal of a season on a penalty shot are Chris Kelly (Oct. 3, 2013, for Boston against the Tampa Bay Lightning) and Mats Sundin (Oct. 4, 2006, for the Toronto Maple Leafs against the Ottawa Senators).