"It's all about confidence. Sometimes I would go into the game thinking twice about shooting. Now, if I'm open, I'm open and I'll shoot it. I've been making them," said Bradley, whose previous high was 20 points. "I was fortunate enough for my teammates to find me in transition and give me the ball and I made shots."
Paul Pierce added 21 points and eight rebounds, Rajon Rondo had 11 assists, and Kevin Garnett finished with 10 points and six assists for the Celtics, who shot 22 for 34 (65 percent) in the first half.
Bradley made his first seven attempts and missed just once in the half.
"I could have scored those layups. I'm being serious," Washington coach Randy Wittman said. "I mean, we didn't have anybody guarding him. When I was a player, if you gave me four layups to start the game, I'd have a pretty good groove on to make some jump shots. He ought to send us a postcard of 'Thank you' or something."
With the win and a loss by Philadelphia at San Antonio on Sunday, the Celtics moved within a half-game of the division lead.
Boston led by as much as 25 before cooling off in the second half. The Celtics allowed Washington to get as close as eight, but ended the threat quickly and won for the third time in four games.
The Celtics had played their last eight on the road, partly because TD Garden hosted the NCAA Tournament East Regional over the weekend. And after their first home game since March 9, the Celtics immediately hit the road again for a game at Charlotte on Monday night.
"Usually that first game is a rough one. You don't play on this court for two weeks, it feels like an away game," Pierce said. "We got off to a great start. That was the key, especially when you come off a big trip."
Jordan Crawford scored 20 points, and Kevin Seraphin had 15 points and 11 rebounds for Washington. John Wall added 12 points and nine assists, and Trevor Booker pulled down nine rebounds. The Wizards played without recently acquired Nene, who had 21 points and 11 rebounds Saturday in a loss at Atlanta.
Bradley's previous high was 20, scored against New York last April. He hadn't scored more than 12 in a game this season and passed that in the first quarter, making his first seven shots. Bradley had 19 at halftime and reached his career high on a 21-foot jumper to open the third quarter, putting the Celtics up 55-34.
"It was great to see him go in," Boston coach Doc Rivers said. "I thought there was a point it was clearly confidence because you see him in practice and he makes them, then he gets in the game and he just needed one to fall."
The Wizards responded to Bradley's jumper with a 13-0 run, shutting out the Celtics for 5:17. Crawford converted a three-point play with 7:56 left in the third to cut it to 55-43, Seraphin scored on a putback for Washington's 11th straight point and then after Pierce turned it over at the top of the key, Crawford hit a long jumper to cut the lead to 55-47.
The game of streaks continued as the Celtics scored the next 10 points. Garnett stopped the drought with a pair of free throws with 5:17 left, Pierce hit a 3-pointer and converted a three-point play, and Bass added a jumper to put the Celtics back up 65-47.
The Celtics led 69-55 at the end of the third and didn't let the Wizards get closer than 10 in the final period.
Washington's 34 points in the first half was just two better than its season low. ... Bradley scored 10 of the Celtics' first 15 points ... The Celtics led 27-12 after the first period. ... Greg Stiemsma added 10 points for the Celtics. ... Both teams had 15 turnovers.