Rantanen scored his first of the playoffs to put Colorado back in front 4-3 at 4:11, redirecting a Devon Toews point shot past Connor Hellebuyck.
He made it 5-3 at 8:01, finishing off a cross-crease pass from Nathan MacKinnon on a two-on-one rush.
Josh Manson added an empty-net goal 19:58 for the 6-3 final.
Valeri Nichushkin, Yakov Trenin, and Artturi Lehkonen also scored for the Avalanche, who won four straight games after losing Game One. Alexandar Georgiev made 33 saves. MacKinnon and Toews each had two assists.
Colorado will play the winner of the series between the Dallas Stars and Vegas Golden Knights. Their series is tied 2-2 and continues with Game Five in Dallas on Wednesday.
Kyle Connor, Josh Morrissey and Tyler Toffoli scored for the Jets, who were the No. 2 seed from the Central Division. Hellebuyck made 26 saves.
Connor gave the Jets a 1-0 lead 1:15 into the first period. Avalanche defenseman Josh Manson attempted to clear Connor’s rebound from the crease, but it deflected off Lehkonen and in.
Nichushkin tied the game at one at 3:18, taking a seam pass from Toews from the left point and scoring with a one-timer from the bottom of the right face-off circle.
Trenin pushed it to 2-1 at 5:42 of the second, collecting a loose puck at the net front and beating Hellebuyck.
Morrissey tied it at two at 6:48 on the power play with a one-timer from the point.
Lehkonen made it 3-2 Avalanche when his centering pass went in off Jets defenseman Neal Pionk’s stick blade at 13:45.
Toffoli tied it 3-3 at 2:06, taking a drop pass from Nikolaj Ehlers as he entered the offensive zone and beating Georgiev under his blocker with a wrist shot.
