Jake Allen made 19 saves for the Devils (26-22-2), who have won four of five, including 2-1 in overtime at the Calgary Flames on Monday.
Matt Savoie scored for the Oilers (25-18-8), who were looking to win three in a row for the first time this season. Tristan Jarry made 15 saves in his first home start since being acquired in a trade with the Pittsburgh Penguins for Stuart Skinner on Dec. 12.
Gritsyuk put the Devils ahead 1-0 at 5:23 of the second period. He received a centering pass from Glass at the edge of the left circle and scored with a one-timer that snuck under Jarry’s glove arm.
Savoie tied it 1-1 at 7:02. Following a face-off win by Jack Roslovic, Savoie skated to the front of the net and deflected Jake Walman’s slap shot from the right point under Allen.
Glass responded back for New Jersey to make it 2-1 at 8:32. Catching Oilers defenseman Darnell Nurse on a bad line change, Glass skated all alone down the left wing before taking a pass from Gritsyuk and beating Jarry blocker side from the circle.
Edmonton outshot New Jersey 11-3 in the third period.