Chris Johnson appeared to hit the game-tying 3-pointer with 0.9 seconds remaining but stepped out of bounds before attempting the desperation shot. James Anderson made two free throws a half-second later to seal Philadelphia's win.
Kelly Olynyk scored 28 points to lead the Celtics. Jeff Green had 27 points and Avery Bradley added 23. Rajon Rondo finished with eight points, 14 assists and 11 rebounds.
Carter-Williams had a key steal and pass to Wroten in the final minutes which led to Wroten making two free throws in helping keep the Sixers ahead in their final home game of the season.
Philadelphia led by 19 points in the second quarter, but Johnson hit 3-pointers on consecutive Boston possessions to trim the deficit to two as part of a 14-3 run to close the third quarter.
After an 11-4 Philadelphia run to open the fourth quarter, Boston again got within two points several times down the stretch but could never pull even.
Philadelphia took three of four games from Boston in winning the season series for the first time since 2006-07.
The banged-up Celtics played without Jared Sullinger (left ankle sprain), Jerryd Bayless (hyperextended right knee) and Kris Humphries (sore right knee).
After missing the past two games with a strained left shin, Rondo returned to action and dominated the game's first five minutes before Thaddeus Young's elbow to the head forced him to briefly leave the game.
Rondo had five assists in the first 5:08 as Boston took an early 16-7 lead.
But the minute the Celtics' floor general left the game, the Sixers took over and outscored the Celtics 60-34 the rest of the half.
Casper Ware made a long 3-pointer to cap a 22-9 run that put Philadelphia up by four late in the first quarter. Rondo, who returned late in the first quarter, followed suit by driving for a layup and drawing a foul. He then rebounded his own miss at the line and put the ball right back up for another two to erase the lead in 10 seconds.
The 76ers turned it on again in the second quarter, this time going on a 28-8 run to build a 19-point lead highlighted by Young's steal and ensuing cross-court pass to Wroten for an uncontested slam dunk.
Green led all players at the half with 14 points, but Carter-Williams paced Philadelphia with 12 points and eight assists as the 76ers took a 67-50 lead at the break.
NOTES: The Sixers scored 46 of 67 first-half points in the paint to the Celtics' 18. ... The Celtics are the only team the 76ers have beaten more than once this season. The Sixers could make it two with a win in Miami in their season finale on Wednesday. ... Boston concludes its season Wednesday at home vs. Washington. ... Philadelphia finished 10-31 at home.