Angle, who homered in the first, then laid down a bunt on a low-and outside pitch as Hudson took off from third, scoring easily on the play and handing Baltimore the lead.
Kevin Gregg made it hold up in the bottom of the ninth with his 22nd save and Pedro Strop (2-1) was credited with the win despite allowing the Tigers to tie it in the eighth on Jhonny Peralta's RBI single.
Detroit starter Justin Verlander failed in his bid for a 25th win, settling for a no-decision after allowing five runs on seven eight hits over seven frames, snapping his streak of 12 straight starts with a win.
Miguel Cabrera went 3-for-4 with a solo homer for the American League Central champion Tigers.
Swim Week Miami Beach 2014 [PHOTOS]