Kotalik fired a shot from the bottom of the left circle that clipped Ducks defenseman Scott Niedermayer's stick and caromed up and over goalie Jean-Sebastien Giguere, inside the left post at 2:14.
"We were hitting crossbars, posts," said Kotalik, who struck iron twice before scoring. "We stayed with it, stayed patient and we knew we'd have the strength and conditioning to win it in the third period. We did it."
New York, 4-0 since a season-opening loss at Stanley Cup champion Pittsburgh, earned the victory in Sean Avery's season debut following a knee injury during training camp. Avery played his annoying style and goaded Ducks defenseman Ryan Whitney into a roughing penalty 1:34 into the third, setting up Kotalik's winning score.
Giguere finished with 35 saves, but had little chance to stop Kotalik's drive.
"It's a tough play," Niedermayer said. "You try to get in front of shots, but at the same time if you deflect them by the goalie it's no good, either. It's a tough one the way Giggy was playing. It was probably better to just let him deal with it because he played real well."
Valiquette stopped 11 shots in the second period after a quiet start and earned his fourth NHL shutout and 15th career victory.
Little-used forward Artem Anisimov scored his first NHL goal with 5:38 left during another power play to make it 2-0, with an assist from Avery. That goal was set up by Evgeny Artyukhin's 4-minute, high-sticking penalty.
Dan Girardi sealed the win with a short-handed, empty-netter with 1:59 left.
"We are happy with four wins in a row," Valiquette said, "but we don't want to get too far ahead of ourselves because we know a pat on the back is only a few feet from a kick in the butt."
It was a hard-luck loss for the Ducks, who were playing for the second straight night with starts less than 24 hours apart. Anaheim rallied from a two-goal deficit in the third period at Philadelphia on Saturday night and won 3-2 in a shootout. All the goals, including the lone shootout tally, were scored by Teemu Selanne. The 39-year-old forward had scored twice in two consecutive games.
"We didn't execute to our level," Ducks coach Randy Carlyle said. "When your hockey club is standing still making plays, it shows they are a little bit worn down. We played last night in an emotional comeback. It's hard to recapture that."
Giguere made his second start of the season while splitting time with Jonas Hiller. The Ducks wrapped up a four-game road trip 2-1-1, but had their 12-game, road-point streak snapped (9-0-3).
"It's a tough way to finish a good road trip," Giguere said. "I don't think we're happy with the game tonight, but I think we're satisfied with the road trip."
The Rangers dominated on the shot clock, but failed to generate many early scoring chances and struck the goal posts several times.
With the Rangers slated to play three times in four nights, coach John Tortorella gave Valiquette his first start of the season in place of No. 1 goalie Henrik Lundqvist.
Valiquette was barely tested in the first period when New York held a 13-1 shots advantage, but he bailed out teammate Marc Staal in the second. Valiquette stopped Todd Marchant's hard drive from in close after the defenseman turned over the puck in the Rangers zone.
Avery was involved in several scrums, including one at the end of the second period that had officials separating him and Ducks forward Ryan Getzlaf as they traded verbal jabs.
"Avery has his own agenda out there," Carlyle said. "Some of the things he says to people, you can't believe."
It was Valiquette's first shutout since Oct. 17, 2008, against Toronto. ... The Ducks begin a six-game homestand Wednesday vs. Minnesota. ... Marchant was helped off the ice after he slammed into the end boards behind the Rangers net in the third period. ... Anisimov had only 4:16 of ice time in the first two periods. He scored his first NHL point, an assist, Thursday at Washington. ... LW Aaron Voros was scratched from New York's lineup to make room for Avery.
Copyright by STATS LLC and The Associated Press
Arena: Madison Square Garden Location: New York, New York
Referees: Greg Kimmerly, Brad Watson Linesmen: Steve Barton, Brad Lazarowich
Attendance: 18,200 (101.1% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
No scoring this period
No scoring this period
Ales Kotalik (3)
(Power Play) Assists: Michael Del Zotto, Marian Gaborik
Artem Anisimov (1)
(Power Play) Assists: Vinny Prospal, Sean Avery
Dan Girardi (1)
(Shorthanded) (Empty Net) Unassisted