The Reds lost their season-high seventh in a row.
Price was tossed by umpire Jim Reynolds after the exchange of lineup cards. They got into a lengthy argument that carried on as the Indians took the field — the dispute likely stemmed from Friday night, when several Reds were upset with plate umpire Manny Gonzalez's strike zone.
Kluber (2-5) worked around constant trouble, but recorded his third strong start in a row. He allowed nine hits, struck out seven and didn't walk a batter.
Cody Allen pitched the ninth for his ninth save.
Tony Cingrani (0-1) walked Roberto Perez to start the eighth. Following a force play, Jason Kipnis lined a double to left-center that scored Michael Bourn.