The Celtics' Big Three -- Ray Allen, Paul Pierce and Kevin Garnett -- got off to a fast start, but played limited minutes. Allen had nine points, on three 3-pointers in an opening burst, while Pierce had eight and Garnett six.
Williams scored 16 of points in the final quarter as Philadelphia rallied from a 14-point deficit. The 76ers outscored Boston 11-2 in the final 2:07.
Boston took a 16-4 lead, and maintained advantages of five to 14 points until midway in the third quarter.
"It felt good to be back home," Garnett said. "At the start, we shared the ball, and had the tempo, pace and rhythm going. Early, it felt like we never missed a beat."
Boston second-round draft choice Bill Walker had a pair of windmill dunks to help the Celtics take a 54-44 lead at the half.
But the 76ers, who battled Detroit before losing in six games in the playoffs last season, came back, led by Williams, Young and free-agent signee Elton Brand. Philadelphia cut it 75-72 after three quarters.
"This was an important game for us," Brand said. "Boston has those three great stars. This gave us a barometer to see where we are."
Celtics coach Doc Rivers missed the game. He was at his home in Orlando, Fla., attending to a family matter.