Burks scored the last of his 18 points on two free throws to give Utah a 96-90 lead. The Trail Blazers closed to within two on a layup by Nolan Smith with 1:19 remaining, but Wesley Matthews missed a 3-pointer with a second to go.
Derrick Favors scored 15 for the Jazz, who finished the regular season with five straight wins. Utah wound up as the No. 8 seed in the Western Conference and will take on San Antonio in the first round of the playoffs beginning Sunday.
Portland closed out the season on a seven-game losing streak and missed the playoffs for the first time in four years.
J.J. Hickson had 20 points to lead Portland.