Dragic hit 7 of 9 shots and scored 14 points in the first half for the Suns (2-0), who got 15 points from Marcus Morris.
Suns forward Channing Frye, who missed the entire 2012-13 season with a heart condition, was 5 of 6 from the field and scored 14 points in his first preseason appearance. Doctors cleared the 30-year-old days before the start of training camp.
Phoenix led by as many as 19 points in the fourth quarter, but the Blazers were able to get as close as four points during the final 3 minutes.
Portland's Thomas Robinson, who had seven points and six rebounds in 13 minutes, was ejected in the second quarter for throwing an elbow.
The NBA's Rookie of the Year won't be playing internationally for the United States, instead remains loyal to his Dominican roots.
Within just a few hours of Thursday night's NBA draft, the Oklahoma City Thunder are reportedly shopping Serge Ibaka.
LeBron James made it official Thursday, saying he will not play in this summer's Olympics. Carmelo Anthony, DeAndre Jordan, Jimmy Butler and Klay Thompson are among the players who will.