Max Scherzer won his 10th game on his fourth attempt, working around six hits in 6 2/3 innings while giving up Kansas City's lone run.
Jose Valverde walked a batter with two away in the ninth but avoided further damage in picking up his 22nd save.
Raburn hit a two-run homer in the second and Kelly had a solo shot in the ninth. The Tigers won their second straight to remain 1 1/2 games behind AL Central Division-leading Cleveland.
The hard-luck loss went to Danny Duffy (1-3), who surrendered two runs on four hits in six innings.