The Blazers kept the contest close in the first half, but Curry drained two consecutive 3-pointers in the final minute of the second quarter to give the Warriors a nine-point lead at halftime.
Curry carried that momentum into the second half as he finished with 36 points (12-of-23 shooting), seven assists and six rebounds in 35 minutes to guide the Warriors to a 1-0 series lead. He shot 9-of-15 from 3-point range.
Curry boosted the Warriors' lead to 17 after another 3-point make in the third. Klay Thompson, who scored 26 points on 10-of-24 shooting, aided Curry in Golden State's outburst from beyond the arc. The Warriors converted 17-of-33 tries (51.5 percent) from deep.
The Warriors continued to play without star forward Kevin Durant, who missed his second straight game due to a right calf strain. Draymond Green had a double-double with 12 points, 10 rebounds and five assists.
Damian Lillard led the Blazers with 19 points, six assists and four rebounds. CJ McCollum had 17 points, three boards and an assist. The backcourt duo combined to shoot 11-for-31 against Golden State's defense.
Game 2 is Thursday night at Oracle Arena in Oakland, Calif.