Johan Larsson, Evan Rodrigues and Conor Sheary all scored goals for the Sabres, while Alex Nylander turned in the first multi-point outing of his career with a pair of assists. Jack Eichel tallied in the opening round of the shootout.
Carter Hutton made 30 saves to beat his former team, including a couple of key stops late in an overtime period in which the Sabres were outshot 6-1.
Buffalo led 3-1 after Sheary scored on a 2-on-1 feed from Nylander at 7:46 in the second period. David Perron brought St. Louis back within one upon leaving the penalty box later in the period, and Brayden Schenn tied the game on a wrap-around goal at 8:41 in the third.
The squandered lead could have deflated the Sabres, if not for a loud shift from the line of Larsson, Zemgus Girgensons and Kyle Okposo that livened the crowd and created an atmosphere that was reminiscent of the team's early-season success.
"Obviously, we haven't given them much to get up for as of late," Rodrigues said. "But, in the third period especially when there's a few hits being laid and they were up in their seat and cheering, it was definitely nice to see again."
It all happened in a span of less than 30 seconds late in the third period, when all five Sabres who were on the ice managed to deliver loud plays that elicited louder reactions.
Larsson wrestled Jay Bouwmeester to the ice along the boards. Zemgus Girgensons and Kyle Okposo took turns laying checks on Colton Parayko. On the other end, Casey Nelson punished Jaden Schwartz as he forechecked along the end boards.
"It got physical," Housley said. "It all started with Larsson's line, they came out and delivered some hits. Our guys didn't back off. I just liked the way we played after a back-to-back. In Carolina [on Saturday], I just thought our game was in a pretty good spot. We didn't get the result and we haven't gotten the result in the last two weeks.
"I'm happy for our guys. They just continue to battle, fight and they found a way to win tonight."
Hutton battled his way through the overtime period, including a clutch save on a Tyler Bozak attempt from in tight.