DETROIT — White Sox right-hander Lucas Giolito has risen to the level of being good enough on nights when he’s not at his best, which is a good place to be for an aspiring top-of-the-rotation starter.

That was the case for Giolito in his start Monday against the downtrodden Tigers at Comerica Park. He struck out eight and walked two in six innings, but he gave up three runs and eight hits, including a home run and three triples.

Giolito improved to 12-5 with his first victory since June 30 as the Sox won 7-4. It was their third victory in the first four games of their road trip.

It was a mixed bag, but it was a quality start for Giolito, who handed a 4-3 lead to a bullpen that has been one of the best in baseball of late.

‘‘I didn’t have my best stuff today, that was pretty clear,’’ Giolito said. ‘‘Slider wasn’t really consistent. Fastball command all over the place. Just one of those ones where you really grind through it.’’

‘‘As [pitching coach Don Cooper] said, he probably had his ‘B’ stuff tonight,’’ manager Rick Renteria said. ‘‘But he made the best of it.’’

Giolito hasn’t been as dominant as he was before the All-Star break, but this was his fourth quality start in his last five outings.

‘‘My biggest regret from the outing was just not having better focus on executing in certain situations, like really focusing pitch to pitch,’’ Giolito said. ‘‘I think that’s getting a little frustrated with giving up the hits, especially on the 0-2 and 1-2 counts. But at the end of the day, it’s a ‘W.’ We won. I get the win.’’

Handed a two-run cushion before throwing a pitch thanks to a bloop double by Matt Skole into short center, Giolito retired the first five batters he faced, three of them on strikeouts.

But consecutive singles by Travis Demeritte, Victor Reyes and Jake Rogers produced a run in the second, and the Tigers tied the score on an opposite-field homer by JaCoby Jones leading off the third.

The Sox took their two-run lead back in the fourth on an RBI single by Yolmer Sanchez and a run-scoring bloop single by Ryan Goins that landed in the same vicinity as Skole’s Texas Leaguer.

Giolito was perfect in the first and fourth innings but otherwise pitched in heavy traffic, needing two inning-ending double plays to minimize damage.

A leadoff double by Tim Anderson (3-for-5) and RBI singles by James McCann (2-for-4), Jose Abreu (2-for-4) and Jon Jay against reliever Buck Farmer in the eighth put the game out of reach, with Jimmy Cordero, Jace Fry and Alex Colome combining on three innings of one-run relief for a bullpen that has a 2.28 ERA in the last 18 games, among the lowest in baseball during that stretch.

The Sox improved to 49-61 with three games left in the series, including a day-night doubleheader Tuesday.

The Tigers (32-76) have lost 22 of their last 26 games, so Giolito has faced tougher challenges. Working without a good slider is a challenge against any team, however.

‘‘I was leaving it up in the zone a lot,’’ he said. ‘‘The changeups I was executing, I was getting swings and misses almost every time. We really just homed in on the fastball/changeup combination. If I’m throwing my changeup well, then I can kind of become that two-pitch type of guy. And it will still work out. It did, for the most part.’’