Zub snapped a 1-1 tie in the third period with his second goal of the season.
Ostapchuk scored his first career NHL goal that provided the Senators with a brief 1-0 lead in the second period.
Michael Amadio and Matthew Highmore, Ostapchuk’s linemates on the fourth line, had the assists.
Tomas Tatar scored for the Devils, who have lost four in a row and are 2-6-3 in their past 11 games.
Tatar tied it at 1-1 just 1:18 after Ostapchuk’s goal from Curtis Lazar and Luke Hughes. It was Tatar’s fourth goal this season.
Jacob Markstrom stopped 18 saves for the Devils.
New Jersey: The Devils received solid production from their fourth line of Tatar, Lazar and Nathan Bastian. In addition to the goal, the trio combined for seven shots on goal.
Ottawa: Brady Tkachuk, the Senators leading goal scorer, was held in check. He registered just one shot on goal in 18:23 of ice time.
New Jersey outshot Ottawa 16-2 in the first period, but Forsberg kept the game scoreless.
The Senators are 5-0-1 in their past six games.
Ottawa is at the New York Rangers on Tuesday for the second game of a three-game road trip.
The Devils host the Boston Bruins on Wednesday.
