Better still, Kovalchuk and Co. continued climbing up the standings after winning their season-best fifth straight road game with a 4-1 victory over the Buffalo Sabres on Tuesday night.
Kovalchuk, who also had an assist, completed his hat trick by scoring into an empty net. The credit went to Parise, who passed up what would have been an easy goal to set up Kovalchuk in the slot for a one-timer with 9 seconds left.
"Zach's got the empty-net breakaway, and I was just thinking he was going to put it in," Kovalchuk said. "That says a lot about his leadership."
No problem, said Parise, who had told Kovalchuk on the bench earlier in the period that he would do what he could to set him up for No. 3.
"Opportunities for hat tricks don't come very often," Parise said. "I don't think he was expecting the pass."
It was Kovalchuk's 12th career three-goal game. His previous one was three years ago with Atlanta.
Petr Sykora broke a 1-1 tie 1:44 into the third period, and Martin Brodeur stopped 29 shots in helping the Devils improve to 6-1-2 in their past nine games. Though still in sixth in the Eastern Conference, New Jersey moved one point behind division rivals Philadelphia and Pittsburgh.
It's a different story for the Sabres, whose margin for error grows slimmer as they sit 14th in the East. Jason Pominville scored for Buffalo, which has lost two straight following a 5-0-1 run.
Lack of discipline plagued the Sabres, who drew seven penalties that resulted in the Devils scoring two power-play goals.
"I would say half were bad penalties, just flat-out bad penalties," coach Lindy Ruff said.
Buffalo's lack of offense is also troubling.
The Sabres have scored three or more goals in regulation just five times in 20 games. The only consistent line that is producing features Pominville, who extended his point streak to five games. He has four goals and two assists during the spurt.
"We need pucks to go in for different people," Ruff said. "The big thing would've been getting the lead, forced them out of their game. We didn't. We gave them the lead."
The turning point came with the Devils on the power play to open the third period.
After failing to register a shot during a 47-second, two-man advantage, the Devils capitalized while Sabres defenseman Mike Weber was still in the penalty box for cross-checking Parise during a scramble in front as the second period ended.
The Devils continued to get production from their power-play unit which went 2 for 7. They have converted 10 of 33 opportunities over nine games.
Kovalchuk sealed the win with 10:13 left by redirecting rookie Adam Henrique's pass to cap a 2-on-1 break after Sekera misplayed the puck at the Devils' blue line. His first goal was a beauty, as he and Patrik Elias had the Sabres' penalty-killers scrambling. They twice exchanged passes before Kovalchuk finally flipped a shot into the open left side with 35 seconds left in the first period.
Kovalchuk has 13 goals and 13 assists in 17 games.
"Kovi deserves the hat trick," Sykora said. "He's been a force, generating so much offense out there. He's playing really, really fantastic."
The Devils improved to 17-10-1 on the road this season, matching their win total from last season. They have won five straight away from New Jersey for the first time since last Feb. 3-22.
"We haven't played really well at home, so I think you need to play well somewhere if you want to be successful," Brodeur said. "It's been good on the road. We've just got to keep going."
Brodeur improved to 5-1-1 in his past seven starts, a stretch in which he has allowed 12 goals.
Ruff was back behind the bench for the first time in a week since he broke three ribs during a collision with a player in practice. After spending the past three games watching from the press box, Ruff said he intended to wear a flak jacket to protect his sore ribs. ... Devils LW Stephane Veilleux made his debut with the team after being called up from AHL Albany. Veilleux played in Europe last season, and last played in the NHL with Tampa Bay in April 2010. ... The Sabres finished a four-game homestand and will play at Philadelphia on Thursday. They will then kick off another stretch of four straight at home.