Late in the first quarter, Blazers star guard Damian Lillard threw a bounce pass to Curry in the corner. Curry lined up a 3-pointer as Green raced over to contest the shot.
Curry appeared to have an open 3-pointer but Green jumped and swatted the ball away.
Green's block on Curry gave him four rejections in the first quarter. He had six points, three rebounds and two assists in 11 minutes.
Green was averaging 12.5 points, 9.3 rebounds, 7.8 assists, 1.5 blocks and 1.2 steals in the playoffs headed into Game 2.
Portland led the Warriors 31-29 after the first frame. Golden State holds a 1-0 series lead in the Western Conference finals.