Roy finished with 19 points and eight assists, while Outlaw led the Blazers with 23 points. Greg Oden had 17 points and 12 rebounds for his 15th double-double of the season, and added a career-high six blocked shots.
David Lee led the Knicks with 29 points and 11 rebounds.
The Trail Blazers, who had won five straight against the Knicks, were home after losing their last two on a three-game road trip.
Their latest was a 102-93 loss at Oklahoma City on Friday.
The Knicks had lost three straight at Madison Square Garden going into Sunday's matinee game at the Rose Garden. But the losses came against the Lakers, the Cavaliers and the Celtics and going into the slump, and had won five of their last six.
The Trail Blazers let a 17-point, third-quarter lead dwindle away, and the Knicks built on a 15-4 run, capped by Nate Robinson's 3-pointer, to go up 97-84 early in the fourth.
The Blazers climbed back to 105-101 on Roy's layup with 2:15 left. After Al Harrington hit a 3-pointer for the Knicks, Greg Oden and Travis Outlaw each scored to narrow it to 108-105 with 1:10 left - setting up the winning sequence for Portland.
The Blazers remains without starting point guard Steve Blake, who's still nursing a shoulder injury. Coach Nate McMillan said he would be reevaluated for Wednesday's game against the Thunder.
Sergio Rodriguez, who has been starting at point guard during Blake's absence, hit a 3-pointer to put the Blazers up 41-29 in the first half.
The Knicks pulled within 42-40 on Harrington's 3-pointer, then tied it on Jared Jeffries' jumper. But New York couldn't pull out in front, and Portland went on to lead 59-50 at the half.
The Blazers extended their lead to 71-56 in the third quarter on LaMarcus Aldridge's dunk.
Tim Thomas hit a 3-pointer that closed New York to 78-77 before Robinson put the team ahead with his own 3. Thomas added another 3-pointer to start the fourth quarter that gave the Knicks an 85-82 lead.
