OAKLAND, Calif. -- The Oakland Athletics couldn't wait to get in the dugout in the bottom of the seventh inning Sunday.

No, not because they were excited about the possibility of padding their one-run lead.

They would do that one inning later, providing the bullpen a cushion in a 4-2 victory over the Detroit Tigers.

Rather, they wanted to check on the condition of their best pitcher, Rich Hill.

"We had no idea what happened," A's reliever Sean Doolittle admitted after seeing A's manager Bob Melvin and trainer Walt Horn go the mound in the top of the seventh.

"I thought maybe another foul ball caught (catcher Stephen Vogt)," Doolittle noted. "Then when they went to Rich ... we were very anxious, to say the least, when we saw him come off the field."

Turns out, Hill was pulled from the game with what was labeled a "mild" groin strain after he had hung around long enough to benefit from pinch-hitter Billy Butler's two-run single that gave the A's the lead for good in the bottom of the sixth.

The bloop hit capped a three-run inning that rallied the A's from a 2-0 deficit and into their second straight win over the Tigers after a series-opening loss Friday.

"That's a big hit," observed A's manager Bob Melvin. "Not as hard as (his key two-run single Saturday), but he's not trying to do too much against a guy (Tigers reliever Justin Wilson) who gives up hits like that because he pitches inside so much."

Hill (8-3) won his fifth consecutive start.

He acknowledged afterward that the pain had been building since the fourth inning, and Melvin had seen enough after observing Hill walk gingerly around the mound following his third pitch to Jose Iglesias with one on and one out in the seventh.

"He wanted to stay in, but we didn't want to put him in a position where it could get worse," Melvin explained.

Right-hander Ryan Dull came on to retire Iglesias on a popup on his first pitch, then struck out Ian Kinsler to protect Oakland's 3-2 lead.

Righty Ryan Madson and left-hander Doolittle took it from there, aided by an insurance run provided by a Jake Smolinski sacrifice fly in the eighth inning.

"Lights out. That was a lot of fun to see," Hill said of the bullpen's 2 2/3 innings of perfect work with three strikeouts. "When we're in that position to win a game, and we turn it over to the bullpen, you know we're in good hands."

Doolittle recorded his third save with a 1-2-3 ninth.

Hill, who took the mound as the American League leader in ERA at 2.18, allowed two runs on five hits in 6 1/3 innings. His ERA rose to 2.25.

"I'll sleep on it, and hopefully I'll be fine," he said of the injury.

In winning for the fifth time in May, Hill walked three and struck out nine.

The A's trailed 2-0 before getting a huge break in the sixth.

With two outs and nobody aboard, Danny Valencia and Khris Davis reached Tigers starter Mike Pelfrey for consecutive singles.

It appeared the hits would go for naught, however, when Yonder Alonso grounded to second baseman Kinsler, who booted the routine attempt, allowing Valencia to score.

Marcus Semien then walked to load the bases, prompting Tigers manager Brad Ausmus to summon the left-handed Wilson from the bullpen.

That produced Butler as a pinch hitter, and his flare to center field barely eluded an onrushing Cameron Maybin, delivering Davis and Alonso with the tying and go-ahead runs.

All three runs were unearned.

"In my mind, he's the best second baseman in the game," Pelfrey said of Kinsler. "He makes that play every day. Obviously that stuff happens, but he brings it every day."

Pelfrey (0-5) took the loss despite not having allowed an earned run in his 5 2/3 innings. He allowed six hits and two walks, and he struck out three.

"The tough part about it is Pelfrey has been pitching well and we're trying to get him over that hump," Kinsler admitted. "To not come up with that play, it hurts a little bit.

"We just had a couple of bad breaks. I should have come up with that ball. Cam missed the ball in center field by a couple inches and that's the game."

James McCann and Victor Martinez drove in the Tigers' runs with singles in the second and third innings, respectively, to give the visitors their 2-0 lead.

Martinez finished with three of the Tigers' five hits.

Valencia had three hits and scored two runs for Oakland, while Davis had two hits, including the game's only extra-base hit, an eighth-inning double.

Vogt also had two hits for the A's, who out-hit the Tigers 9-5.

NOTES: Despite losing two of three in Oakland, the Tigers finished with a 4-3 edge in the season series. ... Tigers RHP Jordan Zimmermann (strained groin) threw a 25-pitch bullpen session before the game, but manager Brad Ausmus elected against putting him into the rotation for the upcoming series against the Los Angeles Angels of Anaheim. Zimmermann has been scheduled for another bullpen session Tuesday in Anaheim. ... The Tigers will start RHP Justin Verlander, RHP Anibal Sanchez and RHP Michael Fulmer against the Angels. ... Tigers RHP Shane Greene (blister on right middle finger) also threw a bullpen session before the game and is a candidate to come off the disabled list during the Angels series. It is likely Greene will return to the active roster as a reliever. ... Athletics manager Bob Melvin announced that LHP Eric Surkamp would be recalled from Triple-A Nashville to start Tuesday against Minnesota. The A's have demoted RHP Zach Neal, who started Thursday against Seattle, to the bullpen.