Tyson Ross allowed one run over 6 2/3 innings on Sunday and the Athletics avoided a sweep with a 5-1 win over the Indians.
Ross (1-0), who was called up on Tuesday, worked around four hits and five walks and struck out four to secure the victory.
Seth Smith supported Ross with a two-run homer and Cliff Pennington added a pair of RBI for Oakland, which halted a two-game slide.
Justin Masterson (0-2) gave up four runs on six hits and six walks over five innings in the setback while Travis Hafner recorded the lone RBI.
Cleveland won the first two games of this series and concluded its nine-game road trip with a 7-2 mark.