The result put the Western Conference's No. 1 seed, Calgary, on the brink of elimination in the opening round of the Stanley Cup playoffs. The Avalanche lead the best-of-seven series 3-1. Game 5 will be Friday in Calgary.
Shortly after the Flames failed to convert on a power play, the Avalanche raced up the ice, and Carl Soderberg fed Rantanen a cross-ice pass that he one-timed for the winner. Avalanche goalie Philipp Grubauer made 35 saves, while Calgary netminder Mike Smith stopped 49 shots.
After a scoreless first period, Calgary's Elias Lindholm broke the deadlock with a power-play goal 3:25 into the second. Derek Ryan doubled the Calgary lead at 6:58 of the third period. The Avalanche's J.T. Compher scored 72 seconds later on a rebound, then Rantanen tied the game with a power-play goal with 2:50 remaining in regulation.
David Pastrnak scored twice, Brad Marchand added a goal and two assists, and visiting Boston held on to defeat Toronto to even the first-round Eastern Conference playoff series at two games apiece.
Charlie McAvoy had a goal and an assist, and Zdeno Chara and Joakim Nordstrom each scored once for the Bruins, who will host Game 5 in the best-of-seven series on Friday.
Auston Matthews scored twice for Toronto, and Zach Hyman and Travis Dermott each scored once. Morgan Rielly added two assists for Toronto. Tuukka Rask made 38 saves for Boston while Toronto's Frederik Andersen stopped 25 shots.
Rookie Roope Hintz scored his first two career postseason goals as host Dallas cruised to victory over Nashville in Game 4 to even their Western Conference first-round series.
Alexander Radulov and Mats Zuccarello joined Hintz in scoring on the power play, and Andrew Cogliano also tallied for the Stars, whose four goals in the first period were one shy of the franchise record for a single period in the playoffs.
John Klingberg notched three assists, fellow defenseman Esa Lindell had two, and Ben Bishop made 34 saves for Dallas, which travels to Nashville for Game 5 on Saturday afternoon. Pekka Rinne, who made 40 saves in a 3-2 win over the Stars in Game 3 on Monday, yielded four goals on eight shots before being relieved by Juuse Saros (20 saves).