They can outslug the Tigers too.
Moss broke a 3-all tie in the fifth with a solo shot, and Smith's two-run drive later in the inning ended Sanchez's day. It was an impressive offensive show after the teams split two tense, low-scoring games in Oakland.
Oakland can close out the series Tuesday.
"It was exciting for Brandon to get us on the board," Smith said. "It was nice to score some runs and get back on top there."
Sanchez, the American League's ERA leader, allowed six runs - five earned - and eight hits in 4 1-3 innings.
Jarrod Parker gave up three runs in five innings for Oakland, and the Tigers couldn't rally against the bullpen.
Grant Balfour pitched a hitless ninth for the save - and he became involved in shouting with Victor Martinez that caused the benches and bullpens to empty. Martinez had just hit a foul ball out of play when he and Balfour appeared to start jawing at each other.
Martinez started slowly toward the mound, and players from both teams came running out. The situation eventually calmed and no players were ejected.
"It's competition. Everyone gets going a little bit," Moss said. "Balfour's a character on the mound. There are going to be fireworks sometimes."
Coco Crisp had two doubles and a single for the A's.
After a pitcher's duel in Game 2 between Oakland's Sonny Gray and Detroit's Justin Verlander, the A's had Sanchez in trouble almost immediately. They scored a run in the third and two more in the fourth, and although the Tigers finally snapped out of their offensive funk with a three-run bottom of the fourth, Sanchez couldn't keep the ball in the park.
Moss hit a line-drive over the wall in right field to make it 4-3, and Smith's high fly carried over the fence in left-center.
Oakland won the AL West title and had a better record than Detroit, but it was the AL Central-champion Tigers who entered this series with the big names and the big payroll.
Now Detroit needs two straight wins to extend its season. A banged-up Miguel Cabrera made an error at third base that gave the A's their first run, and Detroit's vaunted starting rotation finally slipped in Game 3.
Sanchez allowed 0.45 homers per nine innings in the regular season, the lowest mark in the AL. Oakland took him deep three times; he had not allowed more than one in a start previously this year.
Oakland threatened in each of the first three innings but needed a break to score the game's first run. After Crisp's single to start the third, Josh Donaldson walked. Jed Lowrie and Moss both struck out, and it looked like Sanchez might get out of the inning when Yoenis Cespedes hit a sharp grounder to Cabrera.
The slugging third baseman couldn't come up with the ball and couldn't keep it in the infield, and the error allowed the A's to take the lead.
Oakland made it 3-0 in the fourth. Reddick led off with his first homer since Sept. 15, and Stephen Vogt followed with a triple and scored on Crisp's one-out sacrifice fly.
Vogt was safe when Jhonny Peralta - who moved from shortstop to left field after returning last month from his drug suspension - couldn't make a strong enough throw home.
Peralta was in the lineup for his bat, and he did give the Tigers a boost shortly after his weak throw. After going scoreless for the previous 20 innings, Detroit pushed across three runs in the fourth to tie it.
With men on first and third, Martinez hit an RBI double down the line in right field. Then Peralta added a two-run single to left.
But the A's went right back to work against Sanchez, and through three games, they've been the better team - at the plate, in the field and on the mound.
NOTES: Oakland had lost four straight road postseason games, including two in Detroit last year. ... Cabrera, who has battled problems with his groin, hit a sharp grounder down the line in left field in the first, but he has been slowed so much that he couldn't even try to stretch the hit into a double. Cabrera has reached base in all 27 of his postseason games with the Tigers. ... Donaldson, Oakland's third baseman, went sliding feet first into a short portion of the fence while chasing a foul ball in the fourth. He didn't make the catch, but he wasn't hurt either.