Eovaldi (1-5) made his first start of the year May 29 and has taken a regular turn in the Los Angeles rotation ever since.
He finally broke through against the Diamondbacks, giving up a lone run despite allowing five hits and walking three. His only other major league victory came in his debut last year after being called up late in the season.
Three relievers worked an inning each, with Kenley Jansen striking out the side in the ninth for his 15th save.
It was Arizona's sixth straight loss.
Los Angeles took the lead with a two-run first -- Juan Rivera contributing an RBI double and Luis Cruz driving in the other score with a single.
Scott Van Slyke homered for the Dodgers in the fourth inning and Elian Herrera hit one out in the seventh.
Wade Miley (9-5) gave up all four runs on eight hits over 6 2/3 innings to take the loss.
Los Angeles has won three in a row and four out of five after suffering through a seven-game losing streak.