Coyotes goalie Mike Smith stopped two shots without his stick during a power play in the third period, but Chicago defenseman Brent Seabrook put a rebound past him with 14.2 seconds left in regulation to send the game to overtime.
Hanzal barely nicked Adrian Aucoin's shot on a redirect in overtime to give the Coyotes a 1-0 lead in the best-of-seven series. Game 2 is Saturday night in Arizona.
Jonathan Toews also scored for Chicago in his first game back from a concussion.
SHARKS 3, BLUES 2, 2 OT
Andrew Desjardins tied it for San Jose with 5:16 in regulation, banging in a one-timer from the slot from Tommy Wingels, and Dan Boyle had two assists. Antti Niemmi, who won a Stanley Cup with Chicago in 2010, made 40 saves.
Patrik Berglund scored his first two career playoff goals in the third period for the Blues, the No. 2 seed in the Western Conference.
St. Louis swept the regular season series 4-0 for the first time since 1994-95 and lost only six games in regulation at home during the regular season. The Blues dropped the last two, however, to Phoenix and Columbus after clinching the Central Division.
BRUINS 1, CAPITALS 0, OT
BOSTON (AP) - Chris Kelly scored on a long slap shot 1:18 into overtime.
Braden Holtby made 29 saves for the Capitals.
Tim Thomas stopped all 17 shots he faced for Boston.
The game was physical and scoreless until Thomas turned back a Washington attack early in the extra period. Brian Rolston dropped it for Benoit Pouliot to clear the zone and he pushed it up to Kelly, who slapped it over Holtby's glove for the game-winner.
The reigning Vezina and Conn Smythe Trophy-winner, Thomas had an easy game for much of the night, including a middle period in which Washington managed just two shots on goal.
Instead, the goaltending star was Holtby, a third-stringer making his playoff debut because Tomas Vokoun and Michal Neuvirth were injured. But he kept Washington in the game while the Bruins peppered him with shots.
RANGERS 4, SENATORS 2
NEW YORK (AP) - Marian Gaborik and Brian Boyle scored minutes apart in the second period to break open a tight game, and top-seeded New York opened its first-round Eastern Conference series with a win.
The Rangers, the No. 1 seed in the East for the first time since they won the Stanley Cup in 1994, shook off their 1-2-1 regular-season mark against the Senators and easily dispatched them in Game 1.
Ryan Callahan scored in the first period, Gaborik and Boyle pushed the lead to 3-0, and Brad Richards added a goal in the third for the Rangers. New York will host the No. 8 Senators again on Saturday night before the best-of-seven series shifts to Ottawa for Games 3 and 4.
Henrik Lundqvist was sharp early, stopping Jason Spezza on a partial breakaway and then turning aside Jim O'Brien, who weaved his way through the New York defense before getting off an in-close drive that was knocked away.