Thaddeus Young and Elliot Williams added 15 points apiece for the Sixers, who have won two of four since tying an NBA record with 26 straight losses.
Philadelphia capitalized on 22 turnovers by Boston and overcame a triple-double by Rajon Rondo, who finished with 11 points, 16 assists and 11 rebounds for the Celtics.
Boston has lost seven straight and twice this season to Philadelphia, which has won just 17 games. The Sixers edged the Celtics 95-94 on Jan. 29, then didn't win again until beating Detroit last Saturday to avoid setting the longest losing streak in NBA history.
Jerryd Bayless scored 23 points for Boston and Brandon Bass finished with 12 points and 11 rebounds. Jeff Green added 15 points for the Celtics.
After struggling through the second quarter, the Sixers kept it close until pulling away late in the third and never allowing the Celtics to retake the lead.
Philadelphia closed the third period on an 11-2 run and led 76-71 entering the fourth quarter. The Sixers held Boston without a point for nearly four minutes in the third before Kelly Olynyk ended Boston's drought on a putback with 14 seconds left.
Philadelphia opened the fourth on a 6-2 run and held a nine-point lead three different times before the Celtics made a run and cut the lead to 89-86 on a three-point play by Green with 6:04 left to play.
Carter-Williams got the Sixers running again with a layup, then took a steal in for another layup and scored seven during an 11-4 run that put Philadelphia in command at 100-90 with 2:21 remaining.
After opening the game 2 for 11 and committing seven turnovers in the first quarter, the Celtics overcame the sluggish start in the second period and outrebounded Philadelphia 16-8. Trailing 31-28, the Celtics came up with back-to-back offensive rebounds on one possession before Bayless hit a 3-pointer to tie it.
Notes: The Celtics outscored the Sixers 34-26 in the second period despite making only 10 of 26 shots. ... Boston G Avery Bradley missed his second straight game with a strained right Achilles tendon. ... Rondo had five triple-doubles last season before tearing his right ACL in January and not playing again for nearly a year. He has 19 regular-season triple-doubles in his career. ... Sims' previous high was 20 points against Sacramento last month.