The Panthers squandered two-goal leads in the third period of their previous two losses, at Carolina and Pittsburgh.
"It can't be a coincidence when it happens three games in a row," Bouwmeester said. "You've just got to get it in your head that you can't sit back and wait for bad things to happen."
The Panthers led 4-2 after two periods despite being outshot 30-12. Boston finished with a 48-27 advantage in shots on goal.
"We gave up 48 shots and lots of chances, that's not winning hockey," Vokoun said.
Boston tied it midway through the third period with two goals in a span of 1:38.
Chara scored on a power play at 13:10 when he one-timed a cross-net pass from Sturm. The goal came 14 seconds after Bouwmeester was penalized for shooting the puck over the glass.
Kessel then beat Vokoun, who stopped 44 shots, with a wrist shot from the top of the faceoff circle at 14:48.
"Coming into the third we knew this team had blown two-goal leads the last couple of games," Julien said. "You start doubting yourself and get fragile. We concentrated on getting that next goal and knew they'd probably tighten up after that."
Florida scored three times on seven shots in the second period to extend its 1-0 lead. Kreps scored the final goal with 0.8 seconds left when he beat Thomas on a 2-on-1 with a wrist shot to the short side.
"It was a boost for us," Kreps said. "We had a two-goal lead going into the third period. We've got to make sure we don't lose those games anymore."
Thomas, who came in second in the NHL with a .926 save percentage, was pulled after giving up four goals on 12 shots.
The Panthers broke a 1-all tie with two goals in 2:39 midway through the second period.
Montador scored at 9:32 when he took a centering pass from Olesz in the slot and beat Thomas low to the glove side.
Then after Boston's Marc Savard hit the post with a shot from a sharp angle, Olesz increased Florida's lead at 12:11, beating Thomas with a wraparound goal after holding on to the puck on a 3-on-2 rush.
"There's no doubt Timmy wasn't at his best tonight," Julien said. "When goaltenders have a bad night, you've got to rely on the other guy and Auld [came through] and he ends up getting a win out of this."
Wideman made it 3-2 at 16:13 when he beat Vokoun with a slap shot from the point on a power play.
"I don't know if they're losing their confidence, we just need better performances from certain people," Florida coach Jacques Martin said. "Some guys aren't doing the job right now."
Boston C Savard had two assists. He came in with a league-leading 52 assists. ... Boston LW P.J. Axelsson played his 700th NHL game. ... Boston is now 3-0-1 on a five-game road trip that ends Saturday at Tampa Bay. ... The loss kept Jacques Martin from reaching his 100th victory as Panthers coach. His record with Florida is 99-94-34.
Copyright by STATS LLC and The Associated Press
Arena: BB&T Center Location: Sunrise, Florida
Referees: Don Koharski, Justin St. Pierre Linesmen: Ryan Galloway, Brian Mach
Attendance: 14,992 (77.9% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Jay Bouwmeester (11)
Assists: Bryan Allen, Kamil Kreps
Marco Sturm (20)
Assists: Chuck Kobasew, Dennis Wideman
Steve Montador (6)
Assists: Rostislav Olesz, Gregory Campbell
Rostislav Olesz (10)
Assists: Steve Montador, Ruslan Salei
Dennis Wideman (9)
(Power Play) Assists: Marc Savard, Marco Sturm
Kamil Kreps (6)
Assist: David Booth
Zdeno Chara (12)
Assists: Marco Sturm, Marc Savard
Phil Kessel (15)
Assists: David Krejci, Milan Lucic
No scoring this period
Nathan Horton shootout attempt against Alex Auld with a Wristshot results in a SAVE.
David Krejci shootout attempt against Tomas Vokoun with a Wide of Net results in a MISS.
Olli Jokinen shootout attempt against Alex Auld with a Wide of Net results in a MISS.
Marco Sturm shootout attempt against Tomas Vokoun with a Wristshot results in a GOAL.
Steve Montador shootout attempt against Alex Auld with a Wristshot results in a SAVE.
Phil Kessel shootout attempt against Tomas Vokoun with a Wristshot results in a SAVE.