The Atlantic-Division leading Raptors reached .500 (22-22) this late in the season for the first time since Feb. 10 2004.
"We worked very hard to get to this point and it's going to be even harder," said Bosh, whose team now goes on five-game road trip.
Toronto finished 4-1 on a homestand during which they played four teams with records below. 500.
"It's good be at .500, but our goal is greater than that," Toronto's Morris Peterson said.
Toronto went on a 19-0 fourth-quarter run when Boston went more than 6 minutes without scoring.
Al Jefferson had 20 points and 10 rebounds for the Celtics, who have lost 10 straight -- their longest skid since losing 10 in a row from March 20 to April 7 in 2000.
"We just made a lot of mistakes at the end of the game and it cost us the game," Jefferson said.
Parker's previous career-high was 22 points in the first game of the season on Nov. 1 against New Jersey. The swingman returned to the NBA after playing six seasons overseas, the last two of which he was Euroleague MVP for Israel's Maccabi Tel Aviv.
He made seven 3-pointers against Boston.
The Celtics trailed by as many as 14 points in the first half, but they outscored the Raptors 28-20 in the third quarter. Jefferson scored six straight late in the third to give Boston its first lead of the game.
Peterson's 3-pointer and Bosh's two free throws made it 92-79 with 1:29 remaining.
Toronto coach Sam Mitchell picked official Dick Bavetta to win a foot race with Charles Barkley. "If it was an eating contest I'd pick Charles," Mitchell said. Barkley, known as the Round Mound of Rebound, has challenged the 67-year-old Bavetta to a race at NBA All-Star weekend in Las Vegas. ... Toronto reached .500 for the first time since Nov. 8, when the team was 2-2. ... The Raptors went 13-for-29 from behind the 3-point arc.
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Steph goes off for 33, gets fired up after tech
Stephen Curry tallies 33 points and even gets animated after a technical foul in the Warriors' 15-point win over the Clippers.
Curry has 33 points, Warriors beat Clippers for 8th straight
— Stephen Curry scored 13 of his 33 points in the fourth quarter and the Golden State Warriors extended their winning streak to eight with a 105-90 victory over the Los Angeles Clippers on Sunday.