Tuukka Rask stopped 20 shots for Boston, which took a 1-0 lead on Noel Acciari's short-handed goal in the first period, but then fell behind in the third after Brandon Dubinsky and Pierre-Luc Dubois scored in a span of 13 seconds.
Coyle tied it when he one-timed a backhanded centering pass from Marcus Johansson into the net with 4:35 left to force overtime. He ended it in the extra period by deflecting a shot from Johansson into the net.
Sergei Bobrovsky made 34 saves for the Blue Jackets, who swept the Presidents Trophy-winning Tampa Bay Lightning in the first round.
Game 2 is Saturday night in Boston before the best-of-seven series moves to Columbus for Games 3 and 4.
BLUES 3, STARS 2
ST. LOUIS (AP) - Vladimir Tarasenko scored two goals and St. Louis beat Dallas in first game of the teams' Western Conference semifinal series.
Robby Fabbri also scored and Jordan Binnington made 27 saves for the Blues, who had lost three of four to Dallas during the regular season.
It was Tarasenko's seventh career multi-goal game in the postseason, tying him with Bernie Federko for second-most in franchise history.
Jason Spezza and Jamie Benn scored for the Stars. Ben Bishop made 17 saves.
Game 2 will be Saturday in St. Louis, before the series moves to Dallas for the third and fourth games of the best-of-seven series.
More AP NHL: https://apnews.com/NHL and https://twitter.com/AP_Sports
Copyright 2019 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.