The Royals won for the 17th time in 20 games, while the Marlins are 1-8 in their past nine.
Davis had not pitched since Aug. 2, returning to Florida to be with his family after the death of his stepbrother on Aug. 3.
Davis (6-9) allowed two runs and six hits while striking out three and walking two.
Marlins starter Tom Koehler (3-8) held the Royals hitless until two out in the fourth, when they pieced together four straight hits.
Source: Associated Press