Vokoun stopped 33 shots and recorded his 24th career shutout, helping the Panthers earn a 1-0 victory over the Blues on Thursday night.
Vokoun, who has three shutouts this season, improved to 7-0 against the Blues since the 2004-05 lockout.
"I took some beatings in the past the first couple of years we played them," said Vokoun, who is in his first year with Florida after eight years with Nashville. "You go into every game with the same intention of winning. Whatever happened before, doesn't really matter. Every game starts 0-0 no matter if you've won 100 games or lost 100 games before."
Stephen Weiss scored the lone goal of the game at 1:10 of the second period.
St. Louis' Manny Legace returned in goal after missing four games with a knee injury. He stopped 24 shots.
"We ran into a hot goaltender," Legace said. "We just couldn't buy one tonight."
The loss extended the Blues' losing streak to three games.
"There's no trends," Blues coach Andy Murray said. "You either play good or you play bad. We didn't play good enough tonight."
Florida earned its second win in its past six games. It was the Panthers' fourth consecutive road victory and it is the first time Florida has won four in a row on the road since February 2003.
Neither team was effective on the power play. Florida was 0-for-7 on the power play while the Blues were unable to convert on any of their six chances.
"I think that was the keys with those penalties we took that could have gotten us into trouble," Florida coach Jacques Martin said, "but our penalty killers did a great job and Tomas, again, was outstanding. It was a great performance."
Weiss put in a rebound for the game's only goal. Nathan Horton hit a slap shot from the right circle and it hit the skate of Blues defenseman Matt Walker. An alert Weiss lifted the puck over Legace for the goal.
"I was just buzzing in their zone and it got to Nathan and he just turned and fired toward the net," Weiss said. "I got a nice rebound with pretty much an empty net. I'll take those."
About 90 seconds later, Vokoun thwarted Martin Rucinsky's shot on a breakaway.
Horton was called for a 4-minute high-sticking penalty at 4:39 of the third period. Once Keith Tkachuk finished his slashing penalty, the Blues had a man-advantage for 2:37 but could not score against Vokoun.
"We lost a hockey game 1-0," Murray said. "We're not seeing goals on our power play. We're not seeing the work ethic from our power play that our penalty-killers are giving us. We're also paying some guys some pretty good dollars to make our power play work."
Tkachuk has gone 14 games without scoring a goal and he has just six in 29 games. ... Retired former St. Louis Rams-Seattle Seahawks defensive end Grant Wistrom attended the game. ... Florida LW David Boothe did not dress. He bruised a knee in Tuesday's 2-1 loss to Calgary. ... This was the first time Florida has not played in the Eastern time zone this season. After playing Sunday in Chicago, the Panthers will not leave the Eastern time zone for the rest of the season.