Mark Scheifele's sixth goal of the season early in the first gave him 813 career points as a Jet, passing Blake Wheeler for the most in franchise history.
Jonathan Toews played his last shift of the game midway through the second period, with head coach Scott Arniel saying postgame that Toews "tweaked something."
Kyle Connor scored twice while Connor Hellebuyck picked up his career-high 45th win as the Jets now need just one point in their final three games to clinch the Central.
Neal Pionk scored the winner just 17 seconds into the extra frame as the Jets captured the season series against the team that knocked them out of the playoffs last year.
Connor Hellebuyck became the third-fastest goalie to reach 300 career wins, while Josh Morrissey left the game late in the second period with a lower-body injury.
The Jets led 2-1 in the second before Artturi Lehkonen, Zach Parise and Josh Manson scored to put Colorado in front for good as they evened the series at a game apiece.