NHL scoring leader Alexander Ovechkin got his league-best 46th goal and Brooks Laich also scored for the Capitals, who moved into first place in the mediocre Southeast Division.
Since Boudreau replaced Glen Hanlon 21 games in, Washington has gone 20-10-4 to move all the way up from last place.
"We believe we're a real good team now," Boudreau said. "Individually, I think they believe they're a hard team to beat and that when they go on the ice they can win any game they play."
Mike Knuble, Sami Kapanen and Randy Jones scored for Philly. The Atlantic Division-leading Flyers lost for only the fourth time in regulation in 19 games since they were in last place on Christmas.
Bradley deflected a slap shot by Mike Green past Martin Biron to give the Capitals a 2-1 lead 2:01 into the third period. Bradley hadn't scored in 17 games, dating to Dec. 26. Kozlov beat Biron with a shot from the left circle to give Washington a two-goal cushion.
"I took a step forward and he put it off the pipe and in," Biron said of Kozlov's goal. "It was a pretty good shot."
On a night former Flyers goaltender Ron Hextall became the 19th person inducted into the team's Hall of Fame, Biron struggled for the first time since losing to New Jersey on Jan. 4. He had been 5-0 in his last seven appearances.
Capitals goalie Olaf Kolzig stopped 31 shots to beat the Flyers for the sixth time in eight decisions.
Only two points separate the top four teams in the Southeast, and only Washington (26-24-5) has a winning record. Seven teams in the Eastern Conference have more points than the Capitals and another is tied.
But Washington has come a long way since an overtime victory in Philadelphia in Boudreau's first game on Nov. 23.
"At Thanksgiving, we were here and people had written us off," Kolzig said. "We had Coach come in with a new philosophy and the guys seemed to respond real well. We just kept going."
The ceremony for Hextall took place between the first and second periods. Beloved by Philly fans for his aggressive and feisty style, Hextall got a little emotion during the tribute.
"Big tough guy, huh?" he joked.
Hextall, now an assistant general manager with the Los Angeles Kings, played 11 seasons in Philadelphia over two stints. He ranks first on the team's all-time list with 240 wins and was the first goalie ever to score a goal by shooting a puck into the net.
After a long intermission because of the festivities, the Capitals scored early in the second to go up 1-0. Laich took a pass in stride from Green, skated in and lifted a backhander over Biron's glove.
Knuble scored a power-play goal to tie at 1 late in the second. Daniel Briere set up Knuble's 21st goal with a perfect centering pass from behind the net. Knuble has five goals in the last three games.
Ovechkin scored off his own rebound for a 4-1 lead. The sensational forward is easily on pace to surpass the career-best 52 goals he had as a rookie two years ago.
A disallowed goal by Scott Hartnell that would've cut it to 4-2 proved to be the difference when Jones scored in the final minute to get the Flyers within 4-3.
It was ruled that Hartnell pushed Kolzig into the net before the puck went in.
"I'm not so sure the puck wasn't in the net before all that took place," Flyers coach John Stevens said.
Philadelphia forward Scottie Upshall sustained a high right-ankle sprain and will be evaluated on Thursday. ... Ovechkin has 12 goals and nine assists in 12 career games against Philadelphia. ... The Flyers are 6-4-1 in the second part of back-to-back games. ... Philadelphia is 2-1-1 against the Capitals this season after losing all four meetings last year.
Copyright by STATS LLC and The Associated Press
Arena: Wells Fargo Center Location: Philadelphia, Pennsylvania
Referees: Dave Jackson, Rob Martell Linesmen: Brad Kovachik, Dan Schachte
Attendance: 19,778 (101.4% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
No scoring this period
Brooks Laich (9)
Assist: Mike Green
Mike Knuble (21)
(Power Play) Assists: Daniel Briere, Simon Gagne
Matt Bradley (3)
Assist: Mike Green
Viktor Kozlov (11)
Assists: Tomas Fleischmann, Tom Poti
Alex Ovechkin (46)
Assists: Nicklas Backstrom, Milan Jurcina
Sami Kapanen (5)
Assists: Jeff Carter, Jim Vandermeer
Randy Jones (4)
(Power Play) Assists: Mike Richards, Mike Knuble