Moss hit a one-out homer in the fifth and Smith followed two batters later with a two-run shot in a rally that broke a 3-3 tie and put the Athletics within one win of advancing to the AL Championship Series.
The teams meet in Game 4 of the American League Division Series at 5 p.m. EDT Tuesday. If the Tigers win that game, they will force a Game 5 Thursday in Detroit.
Oakland took a 3-0 lead when Coco Crisp scored on an error in the third inning and Josh Reddick led off the fourth with a home run and Crisp added a sacrifice fly the next inning.
The Tigers came back with three runs in the bottom of the inning, combined four of their seven hits in the game in the rally. Victor Martinez singled in Torii Hunter for the first run and Prince Fielder and Martinez came in on Jhonny Peralta's single to left for a 3-3 tie.
Moss broke the tie with his home run to right and, after Yoenis Cespedes singles, Smith made the score 6-3 with a shot to left-center.
All three Oakland home runs came off Detroit starter Anibal Sanchez (0-1), who was touched for six runs (five earned) and eight hits in 4 1/3 innings.
Jarrod Parker (1-0) lasted five innings in his start for the A's. He allowed five hits and all three Detroit runs. Grant Balfour pitched the ninth, giving up a walk but nothing else, in getting the save.