The 25-year-old Godley was 3-0 with a 1.50 ERA and 17 strikeouts in three starts during a previous stint with the Diamondbacks this season. He is the second Arizona starter to win his first three starts in the majors, with Anderson in 2014.
Anderson was Arizona's best starter the first two months of the season, but has struggled lately. The 27-year-old had a stint on the disabled list and has allowed four earned runs in six of his past eight starts.
Anderson is 5-5 with a 4.51 ERA in 21 starts this season after allowing five runs in 4 1/3 innings against Pittsburgh on Tuesday night.