Crosby batted a shpt out of the air and past goalie Brian Elliott in the second period for his first goal, tapped in one from the doorstep against Petr Mrazek 7:41 into the third and then deflected in another just over three minutes later.
Jake Guentzel had a goal and three assists for Pittsburgh. Bryan Rust and Carl Hagelin also scored. Matt Murray stopped 24 shots for his third straight playoff shutout.
Game 2 is Friday night in Pittsburgh.
Elliott stopped 14 of 19 shots and was pulled in favor of Mrazek after Crosby's latest bit of wizardry pushed Pittsburgh's lead to 5-0 just 9:01 into the second. Mrazek wasn't much better, getting beaten by Crosby twice more as Philadelphia's return to the playoffs after a one-year absence started with a thud.
at Winnipeg 3, Minnesota 2: Defenseman Joe Morrow broke a tie with 6:13 left and Winnipeg beat Minnesota n Game 1 for the first playoff victory in franchise history.
In its only other playoff appearances since joining the NHL in 1999 in Atlanta, the franchise was swept in 2007 by the New York Rangers and 2015 by Anaheim.
Nikolaj Ehlers set up the Morrow at the point for a one-timer that beat goalie Devan Dubnyk. Morrow was acquired at the trade deadline from Montreal in exchange for a fourth-round draft pick this summer.
Mark Schiefele, with a power-play goal, and Patrik Laine also scored for Winnipeg, and Connor Hellebuyck made 18 saves. Matt Cullen and Zach Parise scored for Minnesota, and Dubnyk stopped 37 shots.
Game 2 is Friday night in Winnipeg.