Lillard, who was also credited with seven assists, helped carried the load for the Blazers while LaMarcus Aldridge sat out a second game with a strained groin.
Enes Kanter led the Jazz with 25 points and 10 rebounds. Trey Burke contributed 21 to the effort.
Portland prevailed despite shooting a modest 42.9 percent from the field compared to 45.1 percent for Utah in a game that featured 19 lead changes. The Blazer led 15-16 after one quarter.