DETROIT — It’s one of the happiest sounds in baseball, and Ryan LaMarre made it happen in the White Sox’ 6-3 victory Tuesday night.

A group of cheering, screaming fans from the visiting team, easily heard in an otherwise quiet stadium, can only mean one thing — a rare home run by a friend and family member.

How rare?

For LaMarre, who connected against Tigers left-hander Blaine Hardy in the second inning to break a 3-3 tie, it was the first long ball of the 29-year-old outfielder’s undistinguished 80-game major-league career. And he did it at Comerica Park, a 60-minute drive from Jackson, Michigan, where he grew up rooting for the Tigers, and a 45-minute ride from Ann Arbor, where he starred as an outfielder for the Wolverines.

A group of 40 to 50, including LaMarre’s wife and parents, on their own Sox island in Section 128 on the lower level behind home plate, cheered with everything they had. For the Sox, a 43-76 team starting to wind down a season that hasn’t produced a whole lot to cheer about, it was a nice, noisy moment.

“I don’t think anyone in the dugout knew it was my first homer,’’ said LaMarre, whose uncle sitting in the left-field stands somehow caught the ball. ‘‘I don’t know if he caught it on the fly or on the bounce, but he wouldn’t give it back [to Sox pitchers in the bullpen asking for it on LaMarre’s behalf]. He was bringing it over to my parents.’’

Also nice: Jose Abreu padding the lead with a two-run double in the fifth inning to make it 6-3. It was Abreu’s 34th double and his 69th and 70th RBI.

Not as nice was Sox right-hander Lucas Giolito’s first inning, in which he allowed three runs after the Sox — getting an RBI single from Daniel Palka and two runs on Kevan Smith’s sacrifice fly thanks to a botched rundown by the Tigers’ infield — had staked him to a 3-0 lead during their first at-bat. The bad opening raised Giolito’s first-inning ERA to 8.63.

Giolito, however, regrouped and strung together five scoreless innings, including a nifty escape from a bases-loaded, no-out jam in the sixth.

“The changeup was good, and this was probably the best my curveball felt all year, throwing it for a strike,’’ Giolito said. “I just made my pitches and got out of it. I was facing the bottom of the order; I knew I had to get ahead and put them away.’’

Giolito had 16 swings-and-misses, a season high, and threw 73 of 99 pitches for strikes while striking out seven and walking one, a season low for an outing longer than 4„ innings.

LaMarre’s homer, which turned out to be the official game-winner, put Giolito (6.15 ERA) in position for his team-high eighth win against nine losses.

The Sox had given LaMarre some extended major-league life when they claimed him off waivers from the Twins after Avisail Garcia went on the disabled list July 10 with a strained right hamstring.

He was sent down and recalled a second time since from Charlotte, where he was batting .220.

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And so it has gone during a nondescript career, which finally featured a major highlight Tuesday for a second-round draft pick by the Reds in 2006.

“You couldn’t draw it up any better, at least for me personally,’’ LaMarre said. “The fact it put us on top and held that way was even more special.’’

Jace Fry pitched a scoreless seventh and eighth, and Xavier Cedeno got the final three outs for the Sox, who snapped a three-game losing streak and won for the second time in eight games.

But it was LaMarre who got the postgame beer shower.

“It’s still burning,” he said. “Somebody must have thrown mouthwash in there, too.”