The Rangers scored three times on the power play after failing to connect in their previous four games.
"The power play helped us tonight," coach John Tortorella said.
Kotalik, who finished last season with the Oilers after being acquired from Buffalo, started the play that ended up with Ryan Callahan scoring on a deflection at 10:36 of the second period to make it 2-0. After Edmonton's Lubomir Visnovsky cut the margin to 2-1 at 14:52, Kotalik restored New York's two-goal lead when he set up inside the left circle and one-timed a perfect pass from Marian Gaborik behind Nikolai Khabibulin at 16:37.
Gaborik made it 4-1 at 7:31 of the third period when he tapped in a loose puck after Kotalik's straightaway power-play blast slithered through Khabibulin's pads and sat in the crease.
Mike Comrie, returning after a bout with the flu, gave the Oilers a little hope when he beat Steve Valiquette with a wrist shot from the lower right circle with 9:35 left. But Valiquette made his best save of the night seconds later, robbing Andrew Cogliano on a deflection that would have made it a one-goal game.
"The last two or three games, I think the effort has been there," Tortorella said. "We just found a way to score a couple of goals tonight."
Tortorella said this might have been his team's best game all season.
"I think we played smart," he said. "I thought we played hard. I thought our forechecking was much better, and I thought we played smart in the neutral zone."
"Smart" wasn't an adjective Oilers coach Pat Quinn would apply to his team.
"We took offensive-zone holding and hooking penalties, and that shows you're not going to compete on a physical basis," he said.
The four-goal outburst was an offensive explosion for the Rangers, who had managed just five goals in their previous four games. They finished with a season-high 39 shots on goal.
"We didn't pass up shots," said forward Christopher Higgins, who scored the Rangers' first goal in the opening period.
Valiquette, a former Oiler, stopped 26 shots in his first start since Oct. 19, when he was lifted in a 7-3 loss to San Jose.
With Henrik Lundqvist getting a night off, Valiquette got plenty of help from his teammates -- the Rangers blocked 28 shots.
"For any backup goaltender, it's important to work hard in practice and be a good teammate," Valiquette said. "If you are, then your teammates will generally rally behind you. If you're a good teammate, the guys will work hard for you. Of course, I try to be as good a person around here as possible and add value any way I can."
The Oilers had scored just once in losing their two previous games, and Quinn was anything but happy with his team's performance.
"We've got guys who are supposed to be goal-scorers who don't put the puck anywhere near the net," he said.
The Rangers outshot Edmonton 14-8 in the first period and got the game's first goal when Higgins finished off a give-and-go with rookie defenseman Matt Gilroy by beating Khabibulin from the slot at 15:28. It was Higgins' second goal of the season and second in two games.
New York's power play then heated up in the second period, scoring on both of its chances as the Rangers took command of the game. Callahan deflected home a perfect pass from rookie defenseman Michael Del Zotto for his first goal in 11 games, while Khabibulin had no chance on Kotalik's blast after a perfect diagonal backpass by Gaborik.
"Our penalty-killing wasn't great, and that cost us the game," Edmonton forward Patrick O'Sullivan said. "Any time you take penalties in the offensive zone, those are the ones that seem to wind up in your net."
Material from team media was used in this report
1 - 0 NYR
Michael Del Zotto
2 - 0 NYR
2 - 1 NYR
3 - 1 NYR
4 - 1 NYR
4 - 2 NYR
Power Play Stats
Power Play %
% on Road
% at Home
Michael Del Zotto
Hi stick - double minor
Michael Del Zotto