Beckett (1-1) and Diamondbacks rookie Tyler Skaggs engaged in a pitchers' duel over the first five innings. Ethier then broke a 1-1 deadlock with a solo homer into the left-field pavilion in the sixth against Matt Albers (0-1).
Beckett, obtained from the Boston Red Sox along with Adrian Gonzalez, Carl Crawford and Nick Punto in a blockbuster deal last week, held the D-backs to one run on six hits over 6 2/3 frames. He walked one and struck out nine.
Hanley Ramirez also homered for second-place Los Angeles, which remained 4 1/2 games behind National League West-leading San Francisco.
Skaggs, making his third major league start, finished by allowing one run on five hits over five frames.
Justin Upton went deep to provide Arizona's only run.