Spencer Hawes and Evan Turner each connected on a pair of free throws in the final minute to turn back the Trail Blazers, who got late baskets from LaMarcus Aldridge and Damian Lillard to stay within two points.
Lillard, however, missed a lay-in as time expired, and the Sixers held on for a fourth straight win to wrap up a six-game road trip.
Turner provided 23 points and Michael Carter-Williams helped out with 16 and nine rebounds.
Aldridge finished with 29 points, 14 rebounds and five blocks, and Lillard added 17 points for Portland, which fell for the third time in five games.
Celebrity Families of 2014 [PHOTOS]