Tampa Bay also got goals from Ondrej Palat and Anthony Cirelli, and Andrei Vasilevskiy made 26 saves.
Hedman, who has five goals and 17 assists this season, has been critical of himself for several defensive miscues recently.
''Good for him,'' Lightning coach Jon Cooper said. ''He's really been working at his game.''
Brandon Saad and Pavel Buchnevich scored for the Blues. Ville Husso stopped 31 shots.
''We competed hard, had the right intentions,'' Saad said. ''At the end of the day, puck management and a couple mistakes cost us.''
St. Louis starting goaltender Jordan Binnington and defenseman Justin Faulk were placed into COVID-19 protocols before the game. They joined center Tyler Bozak, who went on the list Tuesday.
''It's crazy but that's what this year has been,'' Blues center Ryan O'Reilly said. ''It's unfortunate.''
The Blues recalled goalie Charlie Lindgren from Springfield of the AHL, but due to salary cap issues, he can't join the team until Friday. St. Louis had former Grand Valley State player Kyle Konin as the emergency backup goalie. The 23-year old resides in the Tampa area.
Buchnevich scored with the man advantage at 7:16 of the third, and Hedman put the Lightning up 3-2 from just inside the blue line 53 seconds later. Hedman was left alone in the slot and made a nifty move to beat Husso 2:20 later.
''That's what Heddy does, take a game over,'' Cirelli said. ''Heddy can do it all.''
Hedman had a good scoring chance late in the third but came up short in a bid for his first NHL hat trick.
''It was close,'' said Hedman, who scored 10 goals as a youngster. ''We got two points, that's the most important thing.''
Hedman also had two minor penalties during the final period.
Cirelli had a power-play goal early in the third.
The Blues' second-ranked power play converted their second chance when Saad tied it at 1 at 14:07 of the second off a nifty pass from the blue line by Robert Thomas.
Thomas had two assists, giving him 20 overall.
Palat stopped a 10-game goal drought 7:16 midway through the first.
Steven Stamkos, who missed Tuesday's 4-3 overtime loss at St. Louis due to the birth of his son, assisted on Palat's goal and has a point (five assists, seven points) in each of his last five games.
Lightning: Cooper said RW Nikita Kucherov, out since Oct. 19 with a lower-body injury, is ''inching towards'' skating and remains out until probably after New Year's Day.
Blues: Begin a home-and-home series at Florida Thursday night.
Lightning: Start a five-game trip Saturday night at Boston.
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