After having 16 shots on goal in the first period, the Blues had nine the rest of the game.
"I think we ran out of energy, it looked like to me," Blues coach Craig Berube said. "Execution was off. I think that was a big part of it, not very good execution."
The Blues lost forward David Perron at 11:54 of the first when he left with an upper-body injury after being hit by Blackhawks defenseman Jake McCabe. Perron's head hit the glass, and he fell to the ice but skated off on his own. There was no update on him after the game.
St. Louis, which used 11 forwards and seven defensemen, was down to 10 forwards after Perron was injured.
"We've got a deep team," Thomas said. "We've got a lot of guys who can play with anyone, so that's not an excuse. We've got to be better."
Khaira cut it to 2-1 at 34 seconds of the second period, batting in a rebound in front after Binnington made a glove save.
Hagel tied it 2-2 at 14:56 of the third period when he redirected a point shot by Seth Jones. It was Hagel's third goal in three games.
Chicago center Jonathan Toews had a goal overturned at 4:30 of the first after a coach's challenge by St. Louis for offside. After video review, it was determined Kane entered the zone ahead of the puck. Toews has not scored in 20 games this season after not playing last season because of chronic immune response syndrome. He has nine assists.
"You get down two, they called the offside call, which was the right call," King said. "We looked at it and it's fair. But we didn't get rattled by it. I thought we'd kind of sit back and go into a shell again, but we just kept playing our game."
The Blackhawks outshot the Blues 10-2 in the third period.
"We're a very desperate team, and every time we jumped over the boards, it was guys winning battles," McCabe said. "That desperation, that urgency, wasn't there right away, but we found it in the third and grinded out two points. Those type of wins really help your club's confidence here moving forward."
NOTES:Blues forward Klim Kostin was scratched with an upper-body injury sustained in practice Thursday, and forward James Neal (undisclosed) missed a second straight game. ... Blackhawks defenseman Wyatt Kalynuk had one shot and one hit playing 9:16 in his first game this season after being out with an ankle injury. ... Jones had two assists, including one on the overtime goal, and was plus-1 in a game-high 28:12 playing his 600th NHL game.