New Jersey established a franchise record by winning its sixth consecutive road game to start a season. The Devils, however, are only 1-4 at home.
Boston's Patrice Bergeron tied it 2:32 into the second period and it remained deadlocked until Zubrus re-directed Parise's shot past Tim Thomas.
David Clarkson scored the first New Jersey goal with 7:35 to go in the opening period.
Yann Danis, signed as a free agent during the summer, made his first appearance in goal for the Devils and stopped 31 shots for the victory. Danis spent last season with the New York Islanders, playing in a career-high 31 games.
New Jersey will try to extend its road winning streak Saturday at Tampa.