After Ramirez dove to catch Alex Gordon's soft liner, Alcides Escobar bunted back to Sale, who fielded the ball and ran toward the plate to tag Abreu for the second out.
Lorenzo Cain struck out swinging to end the frame.
"Sale made a nice play, but it wasn't a good bunt," Royals manager Ned Yost said.
"I saw the ball down," Sale said. "Out of the corner of my eye, I saw he was still halfway down the line. I picked it up and tried to make sure I had the ball in my glove and put the tag on him."
White Sox second baseman Gordon Beckham hit a tie-breaking home run in the bottom half of the inning and Kevin Youkilis added an RBI double as Chicago handed the Royals their third loss in the last four games.
It also was the Royals' sixth straight road loss and 15th in their last 18 games away from Kauffman Stadium. Kansas City is 5-10 in its last 15 games.
"It was that one inning where we had first and third and didn't get it done and then they came back and scored," Gordon said. "Total momentum change right there. Gotta give them credit. They capitalized and we didn't."
The two eighth-inning runs ruined another good outing for right-hander Luis Mendoza, who allowed four runs in 7 1/3 innings. Mendoza (5-8, 4.36 ERA) walked one and struck out five, while Sale (13-3, 2.59) earned the win after giving up only two runs -- both solo homers -- in eight innings.
"Both pitchers threw tremendous tonight," Yost said. "It was a great game. They were both very efficient with their pitches, getting quick outs. They had great tempo, both of them."
Monday's contest followed a July 15 matchup in Kansas City in which Sale also got the best Mendoza. In that outing, Sale tossed eight innings of one-run ball to earn the win, while Mendoza allowed two runs in 7 1/2 innings.
Mendoza has a 3.61 ERA in his last six starts but is just 2-4 in that span.
"He's been great lately," Gordon said. "We just haven't been scoring runs for him."
Billy Butler and Jeff Francoeur each homered for the Royals. Francoeur's came in the fifth, while Butler's, his career-high-tying 21st, came in the seventh.
Butler is hitting .523 (11-for-21) with two doubles, two home runs and seven RBIs in his last six road games, while Escobar is hitting .481 (11-for-21) with two doubles and eight RBIs in his career against the White Sox.
Chicago scored the game's first run in the second inning, when right fielder Alex Rios hit a one-out triple and scored on A.J. Pierzynski's double down the first-base line.
After Kansas City's pair of homers, Konerko answered in the bottom of the seventh with a game-tying solo homer.
"I tip my hat off to Konerko. I want Mendy to go after him in those situations," Yost said. "He ended up getting a pitch a little bit too much in the middle. Konerko's a great hitter and he hit it out of the ballpark. We had a couple of chances, but not a whole lot."