Blackhawks right wing Andrew Brunette netted the opening goal of the game in the first period before the Blues chased Emery with goals by Jamie Langenbrunner, Andy McDonald and Patrik Berglund.
Chicago's Viktor Stalberg trimmed the lead in the second period before Brent Seabrook tied the score at 3-3 in the third.
After a scoreless overtime, Patrick Kane recorded the only goal in the shootout to give his team the triumph and snap the Blues' five-game win streak.
"(They) got up 3-1 on us, but still you see the fight in the locker room and in the team to not give up," Kane said. "It's just a fun team to play for."
The Blues rued their missed opportunity.
"The lead came too easy to us," said St. Louis coach Ken Hitchcock. "We didn't have to work for it, and then when we got on our heels. We couldn't get back off our heels."
The Blackhawks (38-25-8), still playing without captain Jonathan Toews, who has missed 11 games with an upper-body injury, avoided a second straight shootout loss after they fell to Los Angeles on Sunday.
Jaroslav Halak made 43 saves to keep the Blues in the game as Chicago's offense dominated.
The Blues (45-18-8) had not allowed more than two goals in their previous 10 games, during a 9-1-0 stretch.
St. Louis lead the Western Conference while the Blackhawks are in sixth.