Smith had three hits and used his speed to set up the go-ahead run and the Rays took three of four from the Oakland Athletics with a 5-4 victory Sunday.
Smith had a bunt single leading off the seventh and went to third after reliever Daniel Coulombe (0-1) was charged with an error for an errant throw to first that ended up in the right-field corner. Tampa Bay went ahead 5-4 when Corey Dickerson hit a sacrifice fly on the next pitch.
"Just see if he can make a play," Smith said about his decision for the bunt.
The error was Oakland's major league-high 62nd. The Athletics are 9-23, including 1-7 in one-run games, on the road.
"It's been frustrating," Oakland manager Bob Melvin said.
Smith, recalled from Triple-A Durham on Friday to fill in for injured Gold Glove center fielder Kevin Kiermaier, also walked and went 8 for 14 in the series.
"Just another strong game on his part," Rays manager Kevin Cash said.
Kiermaier is expected to miss at least two months with a broken right hip.
Gotta show some love to all the Rays fans who reached out to me to give me their best wishes on the road to recovery. I will be back!!
— Kevin Kiermaier (@KKiermaier39) June 12, 2017
Oakland loaded the bases with one out in the ninth before Alex Colome retired Jed Lowrie and Khris Davis for his 18th save.
Stephen Vogt had three RBIs for Oakland, which has lost eight consecutive road series. The previous time the Athletics had a worst stretch was in 1986 when they dropped nine in a row.
Davis drove in a run with a single in the sixth to put Oakland 4-3, but Colby Rasmus pulled Tampa Bay even in the bottom of the inning with a solo homer.
Vogt had a two-run single in the second and made it 3-0 with a fourth-inning RBI double.
The Athletics lost twice in the series after going up by three runs.
After striking out the first two batters in the fifth, Jesse Hahn allowed five consecutive hits as Tampa Bay tied it at 3.
Smith and Dickerson had consecutive run-scoring doubles before Evan Longoria hit an RBI single.
"I have to do a better job to minimize the damage there," Hahn said. "Even after the first couple hits, I have to do something there to get that next out."
Hahn, winless in his past 10 road starts, allowed three runs and seven hits in five innings.
Archer gave up four runs and seven hits over six innings.
Athletics: RHP Kendall Graveman (right shoulder) resumed playing catch. ... INF Marcus Semien (right wrist) is hitting soft toss.
Rays: RHP Jumbo Diaz (right arm fatigue) was reinstated from the 10-day disabled list and worked a scoreless eighth.
The Athletics had double-digit hits in each of the final three games of the series but won just once. It's the eighth time overall Oakland has lost when getting 10 or more hits.
Archer threw 114 pitches, the 23rd straight time he has reached the century mark. It's the longest stretch in team history.
Athletics: RHP Jharel Cotton (3-6), 0-2 with a 4.15 ERA in his past three starts, goes against Miami RHP Jose Urena (4-2) Tuesday night. RHP Daniel Gossett will be recalled from Triple-A Nashville to start Wednesday's game with the Marlins.
Rays: RHP Jake Odorizzi (4-3) and Toronto RHP Marco Estrada (4-4) are Tuesday night's starters. Odorizzi has allowed a homer in eight consecutive starts.
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