Missing Roy because of a pulled hamstring, the Blazers snapped a seven-game losing streak against Boston and pulled into a tie atop the Northwest Division with Denver.
Finding a way to win without Roy was a confidence boost for the Blazers.
"It was huge for us," Aldridge said. "He's our go-to guy but guys really stepped up and played good tonight. Today we really had to come together."
Paul Pierce scored 28 points, making 14 of 15 foul shots, and Kevin Garnett had 17 points and eight rebounds for the Celtics (28-5), who were at the end of a four-game road trip and have more losses since Dec. 25 than in the previous two months of the season.
"Down the stretch we just made bad plays," said Ray Allen, who scored 12 points. "That's been the theme of the last three games we've lost."
Boston had a franchise-record 19-game winning streak stopped by the Los Angeles Lakers on Christmas and lost to Golden State the next night. The Celtics bounced back with a 108-63 win over Sacramento, but they hadn't lost to Portland since Dec. 9, 2004.
Rajon Rondo had 13 points, seven assists and six rebounds for Boston.
Portland (20-12) is off to its best start since 2002-03, its most recent playoff season. With Roy out, Portland was missing its captain and leading scorer, but the Blazers were the more aggressive team, outrebounding Boston 44-29.
Led by Outlaw, Portland's bench scored 29 points. Boston lost the lead in the third and didn't get it back.
The Celtics intimidated and held Portland to its lowest point total of the season in a 93-78 win in Boston on Dec. 5. Even so, and even without Roy, the Blazers thought they could win at home, where they are 12-3 this season.
"We had to step it up a notch," Blake said. "But if you're going to win a championship, you're going to have to step it up. We have a lot of talented guys that come to play each night and tonight wasn't any different."
Pierce made five free throws to get Boston to 85-83, but Outlaw drove the ball and jammed it over Garnett on the other end. Pierce completed a three-point play for Boston, but Sergio Rodriguez and Rudy Fernandez each made two free throws to put the game away for the Blazers.
Boston led 27-14 in the second quarter after a 14-3 run. Blake, whose 13 points in the first half led all scorers, hit a running 20-footer to get the Blazers within six, and Portland trailed 45-40 at halftime after Outlaw scored twice.
Oden scored to tie the game at 49 early in the third. Boston built a seven-point lead after Rondo made a 3-pointer and two free throws, but Portland went on an 17-4 run that Aldridge capped with a breakaway dunk to put the Blazers up 70-64.
Blake hit a 3 with 5:03 left in the game and Portland led by seven.
"Anytime you are facing a team like this, you have to outscrap them, outwork them, execute and limit your mistakes," Blazers coach Nate McMillan said.
Portland picked up a technical foul at the end of the first half for having six players on the court. However, a basket by the Blazers when they had too many men on the court was not waived off. "If we would have caught the six men on the court before the made goal, there would have been no score," official Mike Callahan said in a statement after the game. Garnett and Aldridge were called for double technicals in the tense final minute of the game. Garnett elbowed Aldridge after a free throw and Aldridge responded by slapping Garnett in the head. Boston made 29 of 31 free throws (93 percent).