"It was just a fastball down and away," Correia said of Alvarez's third-inning home run." It cut back to him. He's one of the more powerful guys you're going to face. I know. I played with him. He's a buddy of mine so he's going to have to owe me something for that one."
The Pirates scored early against Correia, getting a run in the first inning on a bloop RBI single from Chris Dickerson after Michael Martinez reached on a bunt single and Alvarez reached on an infield single.
The Twins tied it up in the first thanks to an error from shortstop Robert Andino on a grounder hit by Brian Dozier. Dozier eventually scored on a sacrifice fly from Josh Willingham after a single from Joe Mauer. But it was all they could muster against Cole, who gave up just one unearned run on three hits over three innings.
Pittsburgh scored three runs in the third, as Correia left the ball up and served up three extra-base hits, including a two-run blast from Alvarez to right-center field. Andino brought home the other run on an RBI double.
Minnesota didn't score again until the fifth, when Aaron Hicks launched a pinch-hit solo homer off left-hander Adam Wilk. It was Hicks' first at-bat since March 4, as he was dealing with right elbow soreness.
Right-hander Vance Worley, who is competing for the fifth spot in Minnesota's rotation, pitched 3 2/3 innings, giving up a two-run homer to Ishikawa in the sixth inning.
The Twins answered with a two-run homer of their own in the bottom of the sixth from Chris Colabello off right-hander Jake Brigham, but it wasn't enough.
Up next: The Pirates will visit the Rays on Thursday at 1:05 p.m. ET, and Jeanmar Gomez will be matched against southpaw Matt Moore. Phil Irwin and Andy Oliver are also expected to pitch for Pittsburgh.
Rhett Bollinger is a reporter for MLB.com. Read his blog, Bollinger Beat, and follow him on Twitter @RhettBollinger. This story was not subject to the approval of Major League Baseball or its clubs.