"We had possession of the puck and I saw TJ Brodie] and went to get into a passing lane and he made a real nice pass to me," Backlund, who scored his 15th goal of the season, said. "[Devils goalie Cory Schneider] is a quick goalie, so I shot it high and quick."
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Brodie finished with four assists; he's the first Flames defenseman to have that many since Dion Phaneuf in a 4-3 win at the St. Louis Blues on Dec. 5, 2008.
"I had a long meeting with Brodie and told him I wanted him to shoot more pucks and not pass so much and make sure he's getting pucks on the net and he gets four assists," Flames coach Glen Gulutzan said. "He didn't listen to me at all so I'm going to take credit for those assists."
Adam Henrique, Pavel Zacha and Kyle Palmieri scored, and Schneider made 34 saves for the Devils (21-21-10). New Jersey has lost seven straight game at home (0-5-2).
"Both teams played with some pace, had some chances," Schneider said. "For us it's tough to have the lead going into the third and not coming away with two points."
Stajan tied the game at 3-3 when he redirected a pass from Brodie from the slot 7:22 into the third.
The Devils were trailing 2-0 but scored three unanswered goals in the second period to take a 3-2 lead. Henrique and Zacha scored in a span of 3:03 midway through the period for a 2-2 tie, before Palmieri gave the Devils a 3-2 lead on a power-play goal with 24 seconds left.
"I don't think you look at it for moral victories," Palmieri said. "It's time to string wins together. A point is nice but we need two points."
Versteeg scored a power-play goal 22 seconds into the second period off a slap shot from the top of the right circle to give the Flames a 2-0 lead.
Monahan scored the 99th goal of his career with Troy Brouwer providing a screen three seconds after a holding penalty to Devils defenseman Ben Lovejoy expired to give the Flames a 1-0 lead 17:15 into the first period.