Anthony Cirelli and Ondrej Palat scored, and Andrei Vasilevskiy made 26 saves for the Lightning (13-5-4), who have won seven of 10.
Brandon Saad scored, Robert Thomas and Scott Perunovich each had two assists, and Ville Husso made 31 saves for the Blues (12-8-3). Goalie Jordan Binnington and defenseman Justin Faulk were placed in NHL COVID-19 protocol before the game.
"It's crazy, but that's what this year's been," Blues center Ryan O'Reilly said. "It's unfortunate, it's out of our control, but we could have won that game tonight. We've got to stick with it, we've got a tough test coming up [at the Florida Panthers on Saturday]."
Hedman made it 3-2 at 8:09 of the third period with his fourth goal of the season, a slap shot from the point. He extended the lead to 4-2 at 10:29 when Blues defenseman Marco Scandella's pass attempt went right to Hedman and he beat Husso top shelf in a one-on-one.
"It was good for Vic," Lightning coach Jon Cooper said. "I'm not sure he's been completely happy with his game these last few games. For him to break out and put a stamp on this one, it was big."
Palat gave the Lightning a 1-0 lead at 7:16 of the first period. Ross Colton had his shot blocked by Blues defenseman Torey Krug, and Palat, trailing on the play, scored on a backhand at the left post.
Saad tied it 1-1 at 14:07 of the second period with a power-play goal. Thomas passed from the right point to the forward on the doorstep for the tip-in.
"We had some good looks on the power play there to tie it up, but at the end of the day, puck management and a couple of mistakes cost us," Saad said. "We competed hard and had the right intentions."