Vokoun stopped 36 shots for his fifth shutout of the season, and the Panthers snapped New Jersey's seven-game road winning streak with a 4-0 victory Tuesday night.
"If you beat a team like that, especially a team that's been on a roll, it's a confidence boost," Vokoun said. "It shows what you're doing works."
The shutout was the eighth of the season for the Panthers, tying Columbus for most in the league.
"The more separation we can get, the better it is for everybody in this dressing room," Vokoun said. "We want to be in a situation where we control where we go or where we don't go and we don't have to wait for somebody to lose a game or go on a losing streak or something.
"There's a bunch of games left and we're in that position now and it's up to us to keep it," he said.
Scott Clemmensen made 24 saves for New Jersey.
The Atlantic Division-leading Devils lost for only the third time in 16 games. Their road winning streak was tied for longest in the NHL this season. Boston won seven in a row on the road from Dec. 12 to Jan. 15.
The Devils were coming off back-to-back one-goal victories over the top two teams in the league, Boston and San Jose.
"We didn't play a horrible game, we just played a team that was a little bit hungrier tonight," Devils center Brian Rolston said. "I'm not making excuses, we obviously have to be better than that. This obviously was not our best effort."
The Devils had won the first two meetings between the teams, 3-1 at New Jersey and 3-2 at Florida.
The loss matched New Jersey's most lopsided of the season.
"They were a team that probably to some degree were measuring themselves up against us, and we didn't play like we needed to play to have success here tonight," Devils coach Brent Sutter said. "I thought emotionally we weren't at the level we have been the last week."
Vokoun, who made his seventh consecutive start in goal, recorded his 30th career shutout. His best save came in the third period on a New Jersey power play when he quickly slid to his right to stop Brian Gionta's one-timer.
Vokoun got some help in the first period when defenseman Johnny Oduya's slap shot from the point bounced off the goal post to his right.
"He's been unbelievable lately," Booth said. "He's been playing really well and that's why we've had success. That's a very good team over there and to shut them out shows how well Tomas has been playing."
The Panthers blew the game open with two goals in a span of 2:28 in the second period.
Leading 1-0, the Panthers got only their second power-play goal in their last 26 opportunities when Zednik scored at 11:27. After Clemmensen stopped Frolik's wrist shot, the rebound went off Booth's stick and right to Zednik, standing alone at the side of the net.
It was Zednik's fifth goal in the last seven games.
Horton made it 3-0 at 14:05 with his fourth goal in five games after Booth's pass from behind the net went off a skate. Horton grabbed the loose puck in front, held it as he skated to his left and then fired a wrist shot over Clemmensen's right shoulder.
Stillman closed out the scoring with 2:54 left in regulation when he one-timed Weiss' centering pass.
Weiss opened the scoring at 4:18 of the first when he grabbed a rebound in the high slot and fired a wrist shot that went in off the post.
"They got some good bounces go their way, especially in our end where a lot of shots were going right to them," Clemmensen said. "At the other end, it's going the other way for us. It was one of those games where you're kind of going uphill against the wind."
Florida improved to 8-0 on Tuesdays and to 21-1-1 when leading after two periods. ... New Jersey played without injured right winger Brendan Shanahan (foot) and defenseman Paul Martin (upper body) for the second consecutive game. ... New Jersey's road winning streak was the second-longest in franchise history behind a 10-game run in the 2000-01 season. ... The game began a stretch when Florida plays a division leader in five of seven games.