Former Blazer Sebastian Telfair's steal led to a pull-up 3-pointer that gave the Suns a 41-35 lead midway through the second quarter. Another former Blazer, Jermaine O'Neal, pushed the lead to 47-35 with a jumper and a pair of free throws to cap a 14-2 Phoenix run.
Luis Scola's 19-foot jumper made it 53-44 for the Suns at the break, but Portland jumped out in the second half and got as close as 63-62 after a long jumper from Lillard.
The Suns answered with a 10-1 run to make it 73-63, but the Blazers again caught up. Lillard's hook shot tied it with 20 seconds left in the third quarter.
Lillard, the No. 6 pick in the NBA draft out of Weber State, went into the game leading rookies with 18.5 points per game. He has 14 games this season with at least 20 points.
Hickson's dunk and free throw to open the fourth quarter gave the Blazers a 78-75 lead. Ronnie Price's layup gave the Blazers an 84-83 edge with 6:28 left, and Lillard added a pair of free throws.
O'Neal is impressed by Lillard, who had 24 points against the Suns earlier this season.
"It's funny because you can't read his face. Sometimes the light which is the glare of being a rookie in the NBA becomes so bright that you see it affect some of the guys emotionally or physically," O'Neal said. "He does a great job keeping his demeanor. He loves the big shot, obviously, he took some big ones. I think he's definitely the future of this team."
The Suns were coming off a 121-104 victory over Charlotte on Wednesday night.
NOTES: Hickson's seven consecutive double-doubles are a career high. The last Blazers player with seven straight was Arvydas Sabonis, from Nov. 4-17, 1997. ... Portland has won seven consecutive regular-season home games against the Suns. ... The Suns beat the Blazers 114-87 earlier this season. ... Dudley had a career-high 10 assists.