Andre Iguodala and Lou Williams each scored 15 and Elton Brand had 14 as the 76ers won their third straight, matching a season high.
Thanks to Speights, Williams and 10 points apiece from Thaddeus Young and Evan Turner, Philadelphia's bench outscored Toronto's 58-17.
Speights finished with nine rebounds, narrowly missing his first double-double of the season.
DeMar DeRozan scored 29 and Andrea Bargnani had 17 as the Raptors lost their ninth straight game. It's Toronto's longest losing streak since a 10-game slide from March 26 to April 12, 2006.
Amir Johnson scored 15 and Jose Calderon had eight points and 13 assists for the Raptors, who have lost 13 of 15 and 22 of 27.
Philadelphia topped 100 points in consecutive games for the first time since doing it in back-to-back losses Jan. 8 at Detroit and Jan. 11 against Indiana.
Calderon returned to the starting lineup after missing Monday's loss to Memphis with flulike symptoms, but Toronto was still without Linas Kleiza, who sat for the fifth time in six games with a sore right knee.
Sonny Weems made his second straight appearance after missing the previous 18 games with back spasms, while Joey Dorsey dressed for Toronto after missing the previous two games with a sore right knee.
DeRozan scored 11 points in the opening quarter as Toronto led 29-20. But Speights came off the bench and almost single-handedly turned that around in the second, scoring 13 points in the first four minutes as the 76ers took the lead with a 14-4 run.
Speights had 17 in the second, one more than his previous season high, but Bargnani's 3-pointer with 13 seconds left made it a 50-all tie at the half.
Williams scored 11 points in the third, including a trio of 3-pointers, and Iguodala added 10 as the 76ers took an 84-77 lead into the fourth.
After its streak of 986 games with at least one 3-pointer end Monday, Toronto's first 3 of the night came from guard Trey Johnson, who signed a 10-day contract before the game. The Raptors went 2 for 8 from 3-point range.
NOTES: The 76ers also won three straight from Dec. 12 to Dec. 15, beating New Orleans, New Jersey and the Los Angeles Clippers. ... Speights scored a career-high 28 points against the Clippers on Dec. 19, 2009. ... Besides signing Johnson, Toronto released G Sundiata Gaines. Johnson was the leading scorer in the D-League, averaging 25.8 points in 26 games for the Bakersfield Jam ... Alexis Ajinca, acquired in Monday's trade with Dallas, made his Raptors debut. ... Bargnani had to head to the locker room late in the first quarter after jamming his toe but soon returned after getting a protective cap put on it.