Perkins walked Abreu on the 14th pitch of the at-bat and Viciedo hit a two-run homer to send the Chicago White Sox to a 7-6 victory over Perkins and the Minnesota Twins in the finale of a doubleheader sweep on Saturday.
Abreu started the winning rally with his leadoff walk against Perkins (3-3). Pinch-runner Jordan Danks was erased when Avisail Garcia grounder into a fielder's choice, but Viciedo drove a full-count pitch over the wall in left for his 21st homer.
"That was probably it more than the at-bat to Viciedo, which I probably threw him six or seven pitches too," Perkins said about the walk to Abreu. "That's tough when you start an inning out like that. I'm trying to get out of there as quick as I can, and the first guy I see is 14 pitches, and I don't get him out."
Trevor Plouffe and Oswaldo Arcia homered for the last-place Twins, who have lost four straight. Pinch-hitter Kurt Suzuki had a tiebreaking RBI double in the top of the ninth against Jake Petricka (1-4).
"We played good enough to win tonight and it's frustrating that they got the ball to me and I didn't get the job done," said Perkins, who has six blown saves.
In the first game, Jose Quintana struck out a career-high 13 and Alexei Ramirez homered to lead the White Sox to a 5-1 victory.
Quintana (8-10) allowed a run in seven innings.
Phil Hughes (15-10) had a career-high 11 strikeouts for Minnesota. He allowed five runs — three earned — in seven innings.
Minnesota got off to a fast start in the second game, scoring four times in the first against Scott Carroll. Arcia had the big blow, a three-run drive to center for his 17th homer.
The White Sox responded with two homers of their own, a three-run shot in the first for Garcia and a solo drive for Abreu in the fifth.
"I was just trying to be too perfect with him because I walked him in the first inning then hung the changeup to Garcia right after him," said Minnesota's Logan Darnell, who allowed four runs, three earned, in 4 1-3 innings. "He's good, especially if he's got the count in his favor."
It was Abreu's first homer since Aug. 22 at the New York Yankees. The Cuban slugger joins Hal Trosky (1934), Ted Williams (1939) and Albert Pujols (2001) as the only major league rookies with 30 doubles, 30 home runs and 100 RBIs.
"Just the bat speed, everything else, it's there," White Sox manager Robin Ventura said. "Everybody's going through little issues of fatigue. It's a long season, but in the end you know he's the guy you want to put your buck on just because he's the guy."
Carroll left the game after five innings due to a torn fingernail on his pitching hand.
Daniel Webb replaced Carroll and allowed a solo homer to Plouffe in the sixth for a 5-4 Twins lead.
The White Sox tied it again on pinch-hitter Conor Gillaspie's two-out RBI single in the seventh.
The doubleheader was scheduled after rain postponed Friday's series opener.
Twins: Darnell pitched in place of LHP Tommy Milone (neck). Milone also missed his last start because of left shoulder fatigue, which he said has improved.
White Sox: Carroll (fingernail) said he's day to day. "They thought it'd be best to call it quits after the fifth and not try to risk further injury," he said.
The Twins have lost two doubleheaders in three days - Sept. 11 to Cleveland and Saturday to the White Sox.
"It was a long day, a tough day and probably about as tough a loss as you'll have," Twins manager Ron Gardenhire said.
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