MINNEAPOLIS -- Finally, the offense that was promised.

Dormant for much of the Twins’ early-season struggles, the bats have roared to life in a trio of blowout wins over the last week, capped by a seven-run outburst in the third inning of Sunday afternoon’s rubber game against Kansas City that powered Minnesota to a 13-4 win at Target Field and a series victory over the American League Central leader.

Andrelton Simmons, Mitch Garver and Alex Kirilloff all homered, while Simmons, Garver, Luis Arraez, Josh Donaldson and Byron Buxton all contributed multiple knocks. Minnesota has won three of its last four games by an average margin of more than eight runs, and the winning series was the club’s first since it took two of three against Detroit from April 5-7.

“We’re in a situation now where we’ve got to win every series pretty much until the All-Star break,” Garver said. “We recognize that. We know how important each pitch is. It’s just a matter of continuing that.”

Kirilloff’s blast, a three-run shot to the right-field upper deck in the eighth, was the fourth of the series for the club’s No. 2 prospect, who has more than made his case to stay on the roster and earn regular playing time once Miguel Sanó returns from the injured list. Kirilloff’s team-leading four RBIs in this game gave him 10 for the season, the most by any player in Twins history through his first 11 career games.

“He’s a good hitter,” manager Rocco Baldelli said. “He was a good Major League hitter the day we called him up and put him out there. We thought he could hit Major League pitching. He’s showing us what he can do.”

In this recent stretch, the Twins reversed course on several of their trouble spots from a prolonged slump.

When they lost 13 of 15 in the second half of April, they couldn’t come through with timely hits or take advantage of opponents’ mistakes, hitting .179 (19-for-106) in that span with runners in scoring position. But in their seven-run third inning on Sunday, they were aided by two errors from Kansas City third baseman Hunter Dozier -- one fielding, one throwing -- and made it hurt with five unearned runs.

After Simmons drove a two-run blast to left for his first homer with the Twins, the club didn’t let up, as Arraez, Donaldson, Buxton and Cruz all reached base before Kirilloff drove a sacrifice fly and Garver capped the rally with a three-run blast to the second deck in left field.

The seven runs in the frame were the Twins’ most since Aug. 20, 2019, when they plated seven in the eighth inning of a win over the White Sox.

“When you grind it out, when you keep hitting balls hard, balls will find spots on the field, and you’re going to end up with guys on base, and you’re going to end up bringing guys home,” Baldelli said. “I think that’s what we’ve seen.”

Garver has now clubbed three homers in his last three starts following a .151/.196/.321 start to the season. A resurgence from the 2019 AL Silver Slugger Award winner is particularly important now with Ryan Jeffers back at the alternate training site, leaving the door open for Garver to assume a greater share of the catching duties.

The Twins also added on in the late innings with three more runs in the sixth, removing any doubt about the outcome after starter José Berríos allowed four runs to pull the Royals within striking distance. That rally featured an RBI triple from Arraez and RBI doubles from Donaldson and Buxton, who hit the hardest batted ball of his career at 115.6 mph on the play.

Kirilloff’s three-run blast in the eighth capped Minnesota’s greatest scoring output since a 15-run outburst on April 5 -- during the team's previous series victory.

Through all of their offensive struggles, the Twins were still making good contact, and they entered Sunday with the second-highest hard-hit rate in the American League.

At last, those balls are landing for hits -- or carrying out of the ballpark.

“I think approaches have been more consistent, one through nine,” Garver said. “Sometimes, the ball hasn’t gone our way over the last few weeks, whether it’s a bloop that’s been caught. We hit a couple balls hard today that were caught also. Some of those things are starting to fall our way, and I think that’s a good sign for things to come.”