Shesterkin helped the Rangers push their winning streak to five games as the Rangers did just enough in a physical game that featured stellar goaltending. Shesterkin registered his 12th regular-season shutout and he earned the game's first star.
Rookie Will Cuylle scored in the second period and Jimmy Vesey added an empty-net goal in the final seconds.
Markstrom made 29 saves and gave the Flames plenty of chances to extend their winning streak to a season-high five games and run their road winning streak to six.
Devils 3, Kraken 1
Tyler Toffoli scored his team-leading 22nd goal of the season as New Jersey extended Seattle's losing streak with a win in Newark.
Jack Hughes and Dawson Mercer also tallied for the Devils, who improved to 2-1-1 since the All-Star break. Nico Daws made 27 saves and held Seattle scoreless for the first 50 minutes of the game.
Will Borgen scored and Joey Daccord stopped 34 of 37 shots for the Kraken, who lost their third in a row overall and sixth straight on the road. Kraken defenseman Brian Dumoulin sustained a lower-body injury on a check by Timo Meier late in the first period and didn't return.
Flyers 5, Coyotes 3
Travis Konecny had a goal and two assists, Morgan Frost scored on a penalty shot and hosts Philadelphia defeated slumping Arizona.
The Flyers won their fourth straight despite going 0-for-8 on the power play. Philadelphia goaltender Samuel Ersson made 20 saves.
Matt Dumba, Matias Maccelli and Alexander Kerfoot scored goals for the Coyotes, who lost their sixth straight (0-5-1). Coyotes goalie Karel Vejmelka stopped 29 shots.
Wild 5, Golden Knights 3
Joel Eriksson Ek scored two goals and Matt Boldy had a goal and two assists to lead Minnesota over Vegas in Las Vegas.
Marco Rossi and Mats Zuccarello also scored goals and Kirill Kaprizov, Brock Faber and Ryan Hartman each had two assists for Minnesota, who won their third straight game. Filip Gustavsson made 27 saves for the Wild, who extended their road winning streak to four games.
Mark Stone, Jonathan Marchessault and Michael Amadio scored goals for Vegas, who had a four-game home win streak snapped. Alex Pietrangelo, playing in his 1,000th NHL game, added two assists. Vegas goalie Adin Hill finished with 24 saves.