After Philadelphia's Andre Iguodala drove for a hook shot with 6.6 seconds left to give Philadelphia a 101-100 lead, Rajon Rondo flipped a long pass to Garnett for the winner.
Garnett then raced to midcourt to intercept the 76ers' inbounds pass.
Ray Allen led Eastern Conference-leading Boston with 23 points, Rondo had 19 points and 14 assists, Glen Davis added 16 points, and Garnett finished with 14. Jodie Meeks led Philadelphia with 19 points, and Lou Williams and Thaddeus Young had 16 each, and Elton Brand added 13 points and 14 rebounds.
Trailing 80-72 with 2:39 left in the third, the Celtics rallied with a 9-0 run - pulling ahead 81-80 lead on Rondo's 3-pointer with 0.9 seconds left in the period to set up the tight fourth quarter.
The Celtics snapped Philadelphia's five-game home winning streak and also handed the 76ers' their second loss in their last six games overall.
Neither team led by more than eight points.
NOTES: Shaquille O'Neal, averaging 11.2 points this season for Boston, missed the game because of a sore right calf, while Jermaine O'Neal sat out with a sore left knee. ... Boston has won 11 of its last 13 games against Philadelphia and leads the series 238-176. ... Brand has seven double-doubles this season - matching his total from 2009-10 - and 368 in his career.