Glass, who also had an assist, scored on a cross-slot pass from Arseny Gritsyuk, immediately after Connor Brown had forced an Ottawa turnover on the forecheck.
Gritsyuk had a goal and two assists, Brown had three assists, Paul Cotter and Simon Nemec each scored, and Jacob Markstrom made 34 saves for the Devils (17-12-1).
Drake Batherson scored twice, Tim Stutzle had a goal and an assist, Dylan Cozens and Brady Tkachuk each had two assists, and Linus Ullmark made 28 saves for the Senators (13-12-4), who have lost five of their past six games (1-5-0).
Ottawa was 3-for-3 on the power play; New Jersey was 0-for-3.
Batherson gave the Senators a 1-0 lead at 1:36 of the first period when he found a loose puck in a scramble around the crease and snuck it past Markstrom’s right pad on a power play.
Nemec one-timed a centering pass from Brown on a rush to tie it 1-1 at 5:09.
Ottawa thought it had taken a 2-1 lead at 9:43 when Batherson redirected the puck into the net with his skate, but video review determined Batherson had scored with a kicking motion and the call on the ice was overturned.
Stutzle put a wrist shot five-hole on Markstrom from the top of the slot on a power play to make it 2-1 at 12:59.
Gritsyuk scored on Brown’s rebound at the edge of the crease to tie it 2-2 at 17:59.
Cotter intercepted a Jordan Spence drop pass at the Senators’ blue line, skated in on a breakaway and slid a backhand between Ullmark’s pads to make it 3-2 at 4:21 of the second period.
Batherson scored his second goal of the game to tie it 3-3 at 10:35. Stutzle forced a turnover in the corner and the puck came to Cozens, who found Batherson in front for a tap-in on a power play.
