But Oden struggled with foul trouble and had just five points with six rebounds in 18 minutes before picking up his sixth on a questionable call with about 4 minutes left.
Kevin Garnett had 14 points and 11 rebounds, and Kendrick Perkins had 12 points and 12 rebounds for Boston, which opened a 25-point lead and almost frittered it away after coach Doc Rivers began resting his starters late in the third quarter.
LaMarcus Aldridge scored 13 points for the Blazers.
Allen, coming off a 21-point game on Wednesday night, scored 10 in the first quarter. But it wasn't until the end of the second that the rest of the Celtics got going, scoring the last 14 points of the half and the first seven of the third quarter to take a 56-36 lead.
They made it 25, 76-51, on Leon Powe's basket to start the fourth before Rivers began substituting liberally and Portland cut the deficit to 11 points. Garnett, who left with 2:20 left in the third, came back in with six minutes left in the fourth and settled things with a couple of big dunks; he also drew Oden's sixth foul.
Oden was the big prize in the 2007 draft lottery, when the Celtics had one of the best chances at landing either him or Kevin Durant, who wound up in Oklahoma City. When the ping pong balls didn't bounce Boston's way, general manager Danny Ainge started dealing and wound up instead with Kevin Garnett and Ray Allen
- the two pieces of the Big Three that led the Celtics to their record 17th NBA title.