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After going 1-8 on their recently completed road trip, the Twins just needed to remember what it felt like to win again.

And in came the Baltimore Orioles, the team with the worst record in baseball. A team with many familiar names, several All-Star appearances and one — shortstop Manny Machado — who will be the big trade target for contenders before the July 31 deadline.

The Twins went out and treated them like the last-place team that they are, sweeping a four-game series — with Sunday’s 10-1 romp the final blow.

The Twins hit .289, averaged 6.5 runs a game, posted a 2.25 ERA and played snappy defense during the four games. It was the kind of all-around play that was expected of them at the start of the season,but has been elusive.

Now, the majors’ next-worst team — the Royals, who are only one game ahead of Baltimore — come to town for three games, and the Twins hope to build momentum. The Orioles are 24-65, Kansas City is 25-64.

“I’m glad how the guys went about their business these last four games, especially after a tough road trip,” second baseman Brian Dozier said after the Twins’ largest margin of victory this year. “But by no means are we done. We have more games left on his homestand before the break, and we have to accumulate some wins.”

The Twins took control of Sunday’s game by erupting for eight runs in the sixth inning, including home runs by Escobar and Dozier. Righthander Jake Odorizzi pitched six shutout innings, outdueling his former Tampa Bay teammate Alex Cobb. And the Twins swept the Orioles in a four-game home series for the first time ever.

“Much needed,” said Paul Molitor, who was freed from high-leverage managing for a change. “Just trying to establish a little bit of something here as we head into our last week before break, and the guys responded. I think there’s been a lot of encouraging signs, from nice starts from the rotation to some bats that contributed — really, everybody that got a chance somewhere along the way the last four days contributed.”

The game was scoreless until the fifth inning, when Mitch Garver blasted a full-count pitch to left for a two-run homer off Cobb.

That was the warmup act for the sixth, in which the Twins tied their season high for runs in an inning.

Dozier opened the inning with a double off the left-field wall, and Escobar followed with a blast to right for his 14th home run of the season. Logan Morrison, tired of Baltimore’s defensive shift in the infield, dropped down a bunt toward third base for a hit. That was also the final pitch for Cobb, who left because of a blister on his index finger.

The rally continued against the Orioles bullpen. Robbie Grossman and Max Kepler followed with singles off Paul Fry, loading the bases. Garver hit a grounder to Machado, who after the game was named to his fourth All-Star team. Machado tried to force out Morrison at home but bounced his throw, and catcher Caleb Joseph pulled his foot off the bag while catching it. Morrison was safe on the error to make it 5-0.

Jake Cave blooped an RBI single. Kepler scored on a Jorge Polanco groundout. Fry struck out Rosario for the second out before getting replaced by Ryan Meisinger, whose 3-1 fastball to Dozier was launched into the second deck in left field, giving the Twins a 10-0 lead.

“It felt like I hadn’t been on the mound for 30 minutes, watching it all unfold,” said Odorizzi (4-6). “There was an injury to Cobb. In that situation, it prolongs things a little bit. Any time you can put eight runs together, I think anybody will sit back and wait until it’s all over with.”