Kennedy (2-2) held the Tigers hitless after giving up a leadoff single to Andres Torres in the bottom of the first. The lefthander pitched his second career shutout and sixth complete game, helping the Devil Rays end a three-game losing streak.
He walked one and struck out six.
Gary Knotts (0-3) nearly matched Kennedy for seven innings, but walked pinch-hitter Carl Crawford to start the eighth and it came back to cost him.
Crawford advanced on Rey Ordonez's groundout and scored when Anderson lined a 2-2 pitch into right field.
Knotts allowed one run and five hits over 7 2/3 innings for the Tigers, who suffered their fifth straight loss.
The Devil Rays got an insurance in the ninth on Toby Hall's sacrifice fly off Chris Spurling.
Detroit, which was blanked for the seventh time this year, had only three runners. Shane Halter reached on an error in the second and Bobby Higginson walked in the seventh.