The Jazz jumped past Phoenix and Houston into eighth place in the Western Conference. Utah has only three games left to play while the Suns and Rockets both have four remaining.
Harris scored 27 points and Hayward made 8-of-11 to produce his 23 points.
Alec Bucks contributed 17 points off the bench in helping Utah to its second straight win.
Portland, which has dropped four straight, was led by Wesley Matthews with 21 points. The Jazz outscored the Trail Blazers by 15 points in the second period to take an 18-point lead at the break.