Marchand used a wrist shot that went through Hedberg's pads to hand the Bruins their third straight triumph.
Tuukka Rask made 25 stops and denied Marek Zidlicky in the top of the sixth shootout round with a sparkling glove save to extend the tiebreaker.
Nathan Horton's tally late in the third period forced extra time as the Bruins improved to 5-0-1 for the best start since 1970-71.
David Clarkson found the net and Hedburg finished with 27 saves as the Devils sustained a second straight loss.
Notable deaths of 2014 [PHOTOS]