Crawford finished with 17 saves.
"There's [nothing] you can do about it; that was tough," Crawford said. "I kind of felt it hit the inside of my pad and from there, I was just hoping that it died. It was a tough bounce, but we've got to feel good about how we played out there."
Game 2 is Friday (8 p.m., NBCSN, SN, TVA Sports 2, CSN-CH, FS-MW).
Blues goalie Brian Elliott made 35 saves, including seven in overtime, in his first solo Stanley Cup Playoff shutout (he shared one with Jaroslav Halak in 2012) and first playoff game since 2013.
"It's a team win first of all, and any time you shut out a team, doesn't matter how you did it, you've got to be happy with that," Blues coach Ken Hitchcock said. "[Elliott] and Jake [Allen] have been the story of the season for us.
"For a 1-0 hockey game, it could have been 6-5. We missed a number of opportunities, they missed a number of opportunities. We didn't hit the net on a number of our quality chances, and they missed the couple open nets, especially late in the game."