The Devils (2-1-0) trailed, 2-1, after two periods, managing only eight shots.
The Devils trailed entering the third period, 5-2, but they scored twice in the first nine minutes.
The Devils now trail in the series, three games to two.
The Devils were trailing by 3-1 heading into the final 20 minutes but they scored four consecutive goals to even their record at 1-1.
And for the 14th time this season, the Devils trailed by two goals.
The Devils trail the two and the final playoff spot by 3 points.
With 13 games left in their season, the Devils trail Ottawa by 9 points for the best record in the conference and the league.
The 21-year-old Burke was not used until the third period, when the Devils were already trailing by four goals.
But the Devils trailed after two periods for only the seventh time this season.
The Devils, once trailed by three goals and twice by two.
