Manager Rick Renteria only had one thing in mind when he went to the mound in the seventh inning Sunday to talk to rookie right-hander Lucas Giolito after the Tigers had loaded the bases with two outs.

‘‘I wanted to see how he felt,’’ Renteria said. ‘‘He said he felt fine. It was very easy for me to leave him in.’’

The next pitch to Jose Iglesias sent chills throughout Guaranteed Rate Field when it sailed toward the left-field line and was called a home run. But the umpires’ review showed that it was foul, and Giolito eventually got Iglesias to ground into the third out.

It was the most dramatic moment of the White Sox’ 7-1 victory, Giolito’s first major-league win.

‘‘When Ricky came out there, he said, ‘How are you doing?’ I said, ‘I’m good, ready to go,’ ’’ Giolito said. ‘‘I really appreciate that I got that opportunity to finish that inning, and luckily we were able to get the ground ball and the out. I felt confident.’’

That’s what Renteria wanted from Giolito (1-1), one of the numerous young prospects the Sox are counting on.

Giolito, who came in the Adam Eaton trade with the Nationals, is only 23. He was a first-round pick by the Nats in 2012 and made six appearances for them last season. He lost to the Twins last Tuesday in his first start for the Sox.

Despite giving up three home runs in that game, Renteria insisted that he liked what he saw in Giolito’s six innings.

Giolito was much better against Detroit, pitching seven scoreless innings and allowing only three hits. He walked three, struck out four and hit one batter.

‘‘His mound presence, that was the biggest thing,’’ catcher Kevan Smith said. ‘‘That was one of the things I personally thought he just needed to work on and get better at, and he showed confidence, he showed perseverance. He battled through stuff without wearing his emotions on his face or looking up to the sky. He just got past it. I loved that about him.’’

Working with four effective pitches and getting ahead of hitters were keys, too. Getting a 5-0 lead courtesy of a five-run third, which featured Matt Davidson’s three-run homer, didn’t hurt.

Renteria said that was a factor in staying with Giolito in the seventh.

‘‘Honestly, he had room,’’ Renteria said, adding that he would have kept Giolito in even if Iglesias’ grand slam had stood up. ‘‘We had room as a team for him to try to maneuver and get out of that particular situation. I guarantee you it was an opportunity for him to learn a little bit more about himself and what he can do the next time around.’’

It continues to be about the future for the rebuilding Sox, and repeating that kind of performance will be important as Giolito moves forward.

‘‘The name of the game is consistency, so I’ve got to see him more and more,’’ Renteria said. ‘‘Obviously, he just got here. I still think his [first] outing was good; obviously [this] outing was good. It always plays better when you come out on top. But there are a lot of guys who can minimize the damage from the other side and come out with losses, and it doesn’t mean they pitched poorly.’’

His teammates like what they have seen so far from Giolito.

‘‘It was a great outing by him, seven scoreless innings,’’ Davidson said. ‘‘It was a great rhythm. That’s what we want to see. The future’s bright.’’

The Sox took the series against the Tigers, their second consecutive series victory against an American League Central rival. They won three games in a five-game series against the Twins to start the homestand.

Follow me on Twitter @toniginnetti.

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