Martinez then made him pay by smashing a pitch off the top of the center field wall, sending both runners home.
Matt Tuiasosopo smacked a solo homer for American League Central-leading Detroit, which took three-of-four from second-place Cleveland and increased its lead over the Tribe to 3 1/2 games.
Drew Smyly (4-0) notched the decision with scoreless ninth and Joaquin Benoit finished up with his seventh save.
Tigers starter Max Scherzer held Cleveland to two runs on seven hits over seven innings.
Lonnie Chisenhall drove in both Indians runs with a second-inning single.