Each highlight ignited a gold towel-waving crowd announced at 37,090, only the eighth sellout at the Oakland Coliseum all season.
Anderson kept the Tigers scoreless behind a sharp breaking ball and a strong defense in his first start since injuring his right side falling awkwardly off the mound at Detroit on Sept. 19. The A's have won six straight at home and will need another surprising sweep in a season full of them.
After dropping the first two games in Detroit, Oakland's return home seemed to light a spark. Anderson needed only eight pitches - seven for strikes - to get through the first.
In the bottom of the inning, Cespedes singled to center to drive home Crisp and give the A's a lead. But with two runners on and no outs, Sanchez came back to strike out Brandon Moss looking and get Josh Reddick to ground into a double play.
Crisp, who had a two-run error trying to make a basket catch on Cabrera's fly in Game 2, stole a long ball from Fielder leading off the second. Crisp jumped against the wall, reached his glove at the top of the fence, and made the grab, forcing a stunned Fielder to stop his trot before second base.
In the fifth, Smith sent a 93 m.p.h. fastball from Sanchez high and far enough to center where nobody could catch it, giving a light fist pump rounding first.
The home run was Smith's third in 15 career at-bats against Sanchez, a midseason acquisition from the Miami Marlins who was steady down the stretch.
Anderson, also making his postseason debut, got Omar Infante to ground into a double play to end the third. The lefty looked in control from the opening pitch, just as he had in six starts after a 14-month absence recovering from elbow ligament-replacement surgery before injuring his oblique.
Anderson went six innings, and gave up just two hits.