Nashville's Shea Weber created a 2-2 tie with 5:25 to go in regulation, but Marchand responded with his 10th of the season to snap the Bruins' two-game skid. The Predators had won their previous two outings.
Nashville took a 1-0 lead into the third period, but goals by Johnny Boychuk and Jarome Iginla put the Bruins in front.
The result made a winner out of Niklas Svedberg, who made his NHL debut for the Bruins and stopped 33 shots. He had been playing for the Providence Bruins of the American Hockey League since signing with Boston in May, 2012.
Mazanec stopped 22 shots in suffering the loss.