The winning streak is Cleveland's longest in 34 years.
Arodys Vizcaino (1-3) walked Tyler Naquin to open the ninth and then walked Juan Uribe on four pitches. With pinch-runner Rajai Davis at first base, pinch-hitter Michael Martinez struck out.
Vizcaino was in danger of issuing another walk when Santana lined a 3-1 pitch to right field, driving in Naquin from second base.
Braves shortstop Erick Aybar mishandled Francisco Lindor's grounder for an error, allowing Davis to score. Jose Ramirez added a run-scoring single up the middle.
Kluber (8-7), coming off a shutout of Tampa Bay, didn't allow a hit through five innings. The right-hander allowed two runs on three hits and one walk with seven strikeouts.
