Clinging to a 1-0 lead in the sixth, the Tribe put Jason Kipnis, Michael Brantley and Carlos Santana aboard with two out and Chisenhall unloaded on a pitch from Jeremy Guthrie, sending it deep into the right field stands for his first career grand slam.
Scott Kazmir (5-4) recorded the victory, yielding two runs on four hits over 6 1/3 innings, walking three and striking out six.
Chris Perez finished up with his 12th save as second-place Cleveland, which came into the game trailing American League Central-leading Detroit by 2 1/2 games, logged a third straight win.
Guthrie (8-7) was tagged for five runs on eight hits over seven innings.
Alcides Escobar drove in two runs for Kansas City.