Curtis Granderson homered and Magglio Ordonez drove in two runs for Detroit, which took two of three from the A's. Oakland has lost 12 of its last 13.
Robertson (7-8) allowed a walk and one run, striking out five in 7 2-3 innings to win for the first time since June 21. Fernando Rodeny finished for his third save in seven chances.
The Athletics threatened in the fourth, loading the bases with two out. But Detroit second baseman Placido Polanco made a leaping snare of Kurt Suzuki's line drive to end the inning.
That began a string of 11 consecutive retired batters for Robertson, ending with Jack Hannahan's double with one out in the eighth. Mark Ellis followed with a single to break up Robertson's shutout.
Rodney came on and got Frank Thomas to ground out, ending the inning.
Erratic Oakland starter Greg Smith (5-11) allowed only one run and three hits in 4 2-3 innings, but walked an unsightly seven batters.
Granderson gave the Tigers a 1-0 lead in the fifth when he led off with his 15th homer, lining an 0-1 pitch from Smith into the right-field stands.
Detroit made it 4-0 in the sixth, beginning with Polanco's bases-loaded single. Ordonez added a two-out, bases-loaded single to drive in two more, all the runs coming off struggling A's closer Huston Street.
The Tigers added two in the eighth on Ryan Raburn's RBI double and a throwing error by pitcher Jerry Blevins on the same play, which allowed Raburn to score.