Pavel Buchnevich sent a cross-ice pass to Snuggerud in the left face-off circle, where he buried a one-timer after Florida had killed 40 seconds of a 4-on-3.
Jordan Kyrou had a goal and two assists, and Justin Faulk and Buchnevich each had two assists for the Blues (20-25-9), who ended a five-game losing streak (0-4-1). Joel Hofer made 16 saves.
Matthew Tkachuk scored twice and had an assist, and Sam Reinhart had a goal and an assist for the Panthers (28-22-3), who had won three straight. Daniil Tarasov made 26 saves.
A.J. Greer put the Panthers up 1-0 at 3:12 of the first period. Luke Kunin fed a pass in front from behind the net, and Greer lifted his own rebound over Hofer's glove under the bar.
Jake Neighbours tied it 1-1 at 4:46 when he took a pass from Buchnevich in stride into the offensive zone and buried a wrist shot glove side on Tarasov.
Kyrou put St. Louis up 2-1 at 7:51. Philip Broberg intercepted a breakout pass from Florida forward Carter Verhaeghe in the neutral zone, skated down the left side and passed to Kyrou, who put a wrist shot in off the right post from the edge of the left face-off circle.
Reinhart evened the score 2-2 with a power-play goal at 9:22, chipping a rebound over Hofer's glove from the slot.
Jonatan Berggren made it 3-2 for the Blues while the teams skated 4-on-4 when he finished a one-handed pass from Faulk with a snap shot from the right circle at 14:27
Oskar Sundqvist increased the lead to 4-2 just 41 seconds into the second period. He rushed up the ice and put a wrist shot on net that squeaked through Tarasov and bounced into the net. It was Sundqvist's first game since Jan. 18, missing the previous four games with a cut on his ankle.
Tkachuk cut the deficit to 4-3 at 16:52, skating in from the right circle and lifting a backhand shot over Hofer's left pad that bounced off the back bar.
It was the first goal of the season for Tkachuk, who was playing in just his sixth game after missing the first 47 following surgery to repair a torn adductor muscle and sports hernia on Aug. 22.
Tkachuk then scored his second of the period while on the power play to tie it 4-4 at 18:39, going to the front of the net and beating Hofer with a wrist shot past the blocker.
St. Louis killed off a double-minor high-sticking penalty on Nick Bjugstad at 11:01 of the third period without allowing a shot on goal.
