Alvan Adams, Walt Davis and Maurice Lucas combined for 56 points, including nine late in the fourth period, as Phoenix outlasted Portland in Phoenix.
Portland, trailing by 18 at halftime, narrowed the gap to 69-64 at the end of the third quarter and took a 75-74 lead on Jeff Lamp's tap-in with 6:39 to go in the game.
The lead seesawed until Lucas completed a three-point play with 3:48 remaining to put Phoenix up 82-79.
A pair of baskets by Larry Nance, combined with Davis' jumper gave the Suns an 88-83 cushion with 1:33 left. But the Trail Blazers, with Mychal Thompson scoring three quick points, got within 90-87 and had the ball with eight seconds remaining.
A three-point goal attempt by Jim Paxson went wide, however, and rookie David Thirdkill sank a pair of free throws with one second left for the final Phoenix points.
The victory in their home opener improved the Suns' record to 2-1. Portland, off to its worst start since the 1975-76 season, fell to 0-3.
Davis finished with 20 points, while Adams had 19 and Lucas 17 with 11 rebounds. Nance had six blocked shots.
Calvin Natt led Portland with 16 points, while Thompson and Paxson had 15 apiece and rookie Lafayette Lever had 13.
Lucas, Adams and Davis combined for 21 of the Suns' first period points as Phoenix shot 75 percent from the field and grabbed a 23-12 lead.
After the Trail Blazers narrowed their deficit to 40-32 with 2:30 remaining in the second quarter, Adams rattled off six points in a 1:31 span to put the Suns ahead 52-34 at halftime.
Lever's steal and layin with 24 seconds left in the third quarter capped a 6-0 Portland string and got the Trail Blazers to within five points entering the final period.