CHICAGO – The Twins were trailing the White Sox once again in the fourth inning Thursday afternoon when Nelson Cruz added a new piece to his uniform.

The designated hitter took the dugout's large orange cooler — presumably filled with ice and hydrating beverages — and emptied it to plop it atop his head in place of his Twins cap.

But this wasn't an avant-garde fashion statement or an attempt at a visual pun about cooler heads prevailing. It was a somewhat desperate attempt to spur his team to avoid a three-game sweep in Chicago.

"He's trying to get something going," manager Rocco Baldelli said. "I don't care what he does. Whatever we can do to get something rolling and get a few runs home, I'll take it."

The Twins did manage one more run. Just not until the eighth inning, and not nearly enough of them.

Chicago did complete the sweep with a 4-2 victory at Guaranteed Rate Field. The White Sox (22-13) lead the American League Central with the league's best winning percentage — 10 games ahead of the Twins (12-23), who have the worst record in the majors.

The loss was the fourth in a row for the Twins on the 1-4 road trip. They have lost seven of eight while continuing to have the same issues — poor clutch hitting, shaky pitching or a combination of the two.

Clutch hitting was an issue Thursday. The Twins loaded the bases twice, in the fourth and fifth innings, but stranded all six runners. In all, they left 12 men on base and went 0-for-10 with runners in scoring position.

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"The opportunities were sitting out there for us," Baldelli said. "We were facing a good pitcher [former Twins starter Lance Lynn]. We went out there, and we made him work really hard. But making him work hard doesn't get us to the finish line, doesn't get us where we needed to be.

"We were in search of a big swing, big hit and a big moment to really put us where we want to be. We didn't see it, and it was frustrating."

Before Cruz's cooler chapeau, the White Sox took a 2-0 lead when Tim Anderson homered in the first inning and Jake Lamb did likewise in the third off starter Michael Pineda (2-2). The Twins got one run back in the fourth when Trevor Larnach doubled and scored on a throwing error by Lynn (4-1), but left the bases loaded when Kyle Garlick flew out.

A two-out double from Jorge Polanco and two walks filled the bases again in the fifth, but Mitch Garver struck out to squander that chance.

The Twins didn't get a hit again until the eighth inning, when Max Kepler homered to cut the lead to 3-2. Willians Astudillo and Garlick followed with singles, but were stranded as Sox closer Liam Hendriks got the last five outs.

BOXSCORE: White Sox 4, Twins 2

Lynn struck out nine and gave up only two hits in five innings. Pineda pitched into the sixth, striking out seven, walking three and giving up four hits. He walked his first two batters of the sixth before leaving for Hansel Robles, who gave up an RBI single to Andrew Vaughn for a 3-1 deficit.

Chicago added an insurance run in the bottom of the eighth off Tyler Rogers. Jose Abreu singled and Vaughn walked before pinch hitter Yermin Mercedes singled Abreu home.

"For me and for everybody, it's a little frustration because we want to win, and we tried everything to win in the game at the end of the day," Pineda said. "And we lost the game."

The Twins, 11 games under .500, return home for a three-game series beginning Friday night against Oakland, which leads the AL West, and a three-game rematch against the White Sox, who have won six in a row.

And Cruz's cooler cap failed to bring any luck. Perhaps a return to 2020's bath robes is in order.