The Twins finally held the Cuban slugger without a hit in what has been a crazy, back-and-forth series through two games.
These teams have traded high-scoring wins in which both have rallied from eighth-inning deficits heading into Sunday's finale, when Gibson looks for a fourth straight road victory.
Gibson (9-8, 3.94 ERA) has posted a 0.86 ERA in winning his last three road starts. He made an adjustment to his delivery before he limited Kansas City to two hits in seven innings in Tuesday's 2-1 road victory.
"The one thing I worked on was loosening my grip a little bit and letting my fingers work," Gibson told MLB's official website. "That seems to be the key, especially with my sinker."
The right-hander's lone start against Chicago (54-57) was last Aug. 9. He gave up three runs in 5 2-3 innings and didn't get a decision in a 7-5 victory that came before Abreu joined the White Sox this year and developed into a sensation.
Abreu had his hitting streak snapped at 21 games Saturday as he went 0 for 3 with two walks - one intentional. It was the longest for a White Sox rookie since Chico Carrasquel's 24-game run in 1950.
He batted .388 while hitting safely in his first 12 games against the Twins (49-60) before Saturday.
''Thank God,'' Minnesota manager Ron Gardenhire said. ''Move the ball in and out. We pitched around him a couple times in situations.''
Slowing down Abreu helped Minnesota erase a two-run deficit in the eighth inning for an 8-6 victory. The night before, the Twins blew a one-run lead in the eighth of a 10-8 loss.
Trevor Plouffe has been the Twins' offensive star in this series, going 7 for 10. He notched his second career four-hit effort Saturday with two doubles and two RBIs.
"We've kind of been resilient all year," Plouffe said. "We'll take the blow and get back up and start fighting again."
Chicago has been led in this series by Adam Eaton, who is 6 for 9 with three RBIs. He's 21 for 43 with 10 runs scored during a nine-game hitting streak, and is batting .388 during an 11-game run versus the Twins.
Eaton's fourth career four-hit effort Saturday, however, was spoiled when he was thrown out trying to stretch a single to close the eighth inning.
"That's ignorant on my part," he said. "That's stupid, unbelievable how dumb that was."
Chicago will hand the ball to Jose Quintana (6-7, 3.15), who is 3-0 with a 1.84 ERA in eight starts since last losing June 13 against Kansas City.
The left-hander failed to receive a decision in four straight outings before yielding two runs over six innings in Tuesday's 11-4 victory at Detroit.
Quintana is 2-2 in eight starts against Minnesota with a 5.36 ERA - his second-highest against any team.
Plouffe has a double in eight at-bats against him while Josh Willingham is 9 for 18 with three homers.