Starting with shortstop Starlin Castro in the bottom of the first.
The Twins met Kyle Hendricks (2-3) with three straight singles and never stopped.
Hendricks, though, had no help behind him.
Castro let a right-to-him ground ball hit by Plouffe get between his legs with the bases loaded as one run scored. Then, while Castro stared and sulked with the ball still in his glove, Eddie Rosario raced home, too. Hendricks flashed Castro an incredulous look, yelling at him to try to get his attention.
"The mistake's on me," Castro said. "Sometimes when those kinds of mistakes happen we lose. You try to eliminate all this. Any excuse for that, it's like my fault. That thing can't happen."
Hendricks offered words of encouragement to Castro between innings and defended his shortstop after the game.
"Everybody makes mistakes," Hendricks said. "I'm up there making mistakes all the time, so there's no way I'm going to criticize guys ever. They made more great plays. Starlin made a great play in the hole later in the game, so I just told him to keep his head in."
After Rizzo's leadoff shot in the fourth cut Minnesota's lead to 3-1, Hughes retired the last 15 batters he faced.
"We needed to hold serve," Cubs manager Joe Maddon said, after his team lost consecutive games for the first time since June 2-3. "We needed to keep it at three to make it more believable. Once it became five, it became less believable. That's to their credit with their add-on runs."
Catcher Miguel Montero's throwing error in the sixth led to another run for the Twins, who won for the third straight time after losing 11 of their first 15 games in June.
"To win ballgames you've got to pitch well and play defense. That's pretty clear," Hendricks said. "But the first part of that's pitching well. I can only do what I can, and regardless of some of those plays, you can't give up 11 hits in five innings."
Hughes (5-6) struck out four without a walk for his first win in four turns, a big boost for a pitcher who was Minnesota's best starter last season but has stumbled a bit while trying to recoup some of his velocity.
"I thought we hit some balls really good and we were kind of a little bit unlucky," Maddon said. "We made a mental mistake early in the game that cost us but other than that it looked more awful than it actually was."
Hendricks has failed to finish six innings in nine of his 13 starts this year, including his last three turns. He allowed 11 hits and a walk while being charged with six earned runs and striking out only one.
"My stuff just wasn't there today. Just one of those days," Hendricks said.
Rizzo has 14 home runs this season, including three in the last three games. This was his second multi-homer game of the year and the ninth of his career.
Mike Olt, the forgotten opening day starter for the Cubs at 3B who's been out since the first week of the season with a broken right wrist, began rehab work on Friday with Double-A Tennessee. Standout rookie Kris Bryant is now entrenched at that position, but Maddon said he wasn't sure if Olt would play elsewhere on assignment.
The Cubs will send LHP Jon Lester to the mound on Saturday afternoon, opposite RHP Trevor May. Lester struck out eight in a complete-game shutout in his last start against the Twins, with Oakland on Aug. 7, 2014. May has a 3.35 ERA and only five walks with 34 strikeouts in his last six turns.