Early allowed just one other hit in six sharp innings, the longest start of his career. Trevor Story drove in five runs to headline another big day for the lineup, and the Sox registered their first come-from-behind victory of the season.

The Twins scored four runs in the ninth inning against Ryan Watson, making the final look closer than the game actually was.

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Heading into a tough homestand against two expected playoff contenders — four games against the Tigers, three against the Yankees — the Red Sox are 7-11. The past two weeks, since they finished that miserable season-opening road trip, they have won as many games as they have lost.

Connelly Early settled down after allowing a first-inning home run and pitched a career-high six innings.Abbie Parr/Associated Press

“We’re [three] weeks into the season, and we feel like we haven’t played anywhere close to our best baseball,” Story said. “And it could be way worse. Once we get rolling and once we get to doing the things that we know we can do on a consistent basis, we’re excited about that.”

Early held the Twins (11-8) to two walks in addition to the two hits. Although he had only one perfect inning — his last — he was efficient and effective throughout, allowing just one runner past first base and collecting five strikeouts.

In four starts this year, Early has a 2.29 ERA in 19⅔ innings.

In four starts last year, he had a 2.33 ERA in 19⅓ innings.

“He looks different out there. He looks just so calm always,” Anthony said. “For a young guy like himself, he looks like he has 10 years [in the majors].”

With everyone wearing No. 42 on Jackie Robinson Day, Trevor Story (right) celebrated with third base coach Kyle Hudson after hitting a three-run home run in the third inning.Abbie Parr/Associated Press

Early is two outs behind Sonny Gray for the team lead in innings pitched and has by far the best ERA of any Sox starter.

In recent weeks, his outings have left him frustrated because he didn’t pitch deep into games, even as he limited opposing offenses.

“It’s super nice to go six,” Early said. “Obviously, the offense did an amazing job working their starter. I feel like that’s the name of the game: If our starter can go longer than theirs, we’re in a really good spot.”

His length continued a weirdly extreme trend for the Red Sox: When their starting pitcher lasts at least six innings, they are 7-0. When he doesn’t, they are 0-11.

Story (2 for 4) led the offense, beginning with a three-run homer in the third inning, the climax of the Red Sox’ five-run rally.

It was the Sox’ first home run with multiple runners on base this season.

In the fifth, Andruw Monasterio had an RBI double and later came in on Connor Wong’s sacrifice bunt.

Minnesota righthander Simeon Woods Richardson gave up 10 hits and seven runs (six earned) across five innings.

Story followed in the sixth with a two-run double to right-center field off lefthander Anthony Banda. That raised his team-high RBI total to 17.

This week, Story has raised his average from .131 to .208.

“It’s good when that right side of the field is in play for me,” Story said. “It seems to open up the left side without forcing it there. So, good signs today and looking to build on that.”

Anthony had two more hits to complete a big series, reaching base nine times in three games. Monasterio totaled three hits and Isiah Kiner-Falefa two in rare starts for both. Jarren Duran (0 for 5, three strikeouts) was the only Sox batter without a hit.

The offensive output was particularly encouraging in the context of a barren-looking lineup. On the bench were first baseman Willson Contreras (low back tightness) and right fielder Wilyer Abreu (rest). Together, they accounted for six of the team’s 11 home runs entering the day.

In the face of Contreras’s unexpected absence — and back-to-back losses, including a shutout Tuesday — manager Alex Cora stuck with his plan to give Abreu a day off. It was the first time this year that he was not in the lineup.

“We got to take care of him. We’re not going to panic here,” Cora said before the game. “I’m not going to throw Wilyer [out there] because, oh, we lost two in a row. No, this is how we do things.”

Tim Healey can be reached at timothy.healey@globe.com. Follow him @timbhealey.