After wrestling for the advantage, Steve Blake put Portland in front 96-94 on a 3-pointer from the corner with 2:41 left. Travis Outlaw made a pair of free throws to extend it and the Blazers led the rest of the way.
Nicolas Batum hit a 3-pointer to make it 101-96 with 29.9 seconds left and seal it. The rookie from France had a career-high 20 points.
LaMarcus Aldridge had 19 points and 10 rebounds for Portland.
Devin Harris scored 27 points for the New Jersey, which has lost five of seven. The Nets were coming off a 116-112 loss at Golden State which denied them a chance to move into playoff position.
The Blazers, among a group of teams tangled in the playoff race, had a statement-making victory over the Los Angeles Lakers on Monday, but then lost 93-89 to Dallas on Wednesday, snapping a 12-game winning streak at home.
The Nets went up 26-20 after Harris' 3-pointer and extended the lead to 42-30 on Vince Carter's jumper.
But the Blazers came back, outscoring New Jersey 15-7, to narrow it to 49-45. The Nets went into the half with a 51-47 lead.
Roy struggled with just one point in the first quarter and just seven points in the half. The two-time All-Star came in averaging nearly 23 points.
After New Jersey jumped out to a 60-49 lead in the second half, Roy hit a jumper for his first field goal of the game.
The Blazers again narrowed it, closing to within 68-65 on Batum's fast-break dunk. But Carter answered with a 3-pointer and the Nets stayed in front until Portland's late run.
The Blazers were without rookie swingman Rudy Fernandez for the second straight game. Fernandez had a bruised chest and a hip pointer from a scary fall he took against the Los Angeles Lakers on Monday night.
Fernandez on a fast break when was fouled by Trevor Ariza and crashed to the floor. He was taken from the floor on a stretcher with his neck in a brace, and was hospitalized overnight.
Batum left the game midway through the first quarter and iced his right shoulder on the bench. He later returned.
Batum hurt his shoulder in the Blazers' loss to Dallas, but MRIs were negative.
Notes: New Jersey Nets forward Eduardo Najera will miss the rest of the season after having surgery Friday to repair a sports hernia. Najera, signed in the offseason as a free agent, played in 27 games, averaging 2.9 points and 2.5 rebounds. ... The Blazers had 10 blocks, matching a season high.
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