Vance Worley was buttoning up his shirt at his locker Sunday, a few feet away from where Mike Pelfrey was describing his relief over having pitched, finally, the way the Twins expected him to when he signed with them. “Was today a breakthrough?” Pelfrey was asked. As the righthander considered the question, Worley slowly nodded his head in agreement.

Worley knows a turning point when he sees one, and Pelfrey’s six-inning, one-run performance in the Twins’ 4-2 victory over the Indians had that look about it. Felt like it in the Twins clubhouse, too, where the sense of relief — hey, he really does have the stuff to shut down a good offense — was hard to miss.

“You hope you’re getting a good pitcher” when you sign him to a free-agent contract, as the Twins did with Pelfrey, manager Ron Gardenhire said. “We think we have a good pitcher who knows what he’s doing. … Hopefully, he’ll keep progressing.”

He meant Pelfrey, but the Twins need similar progress from Worley, too. General Manager Terry Ryan believed he had addressed the biggest reason for last season’s collapse, starting pitching, by signing Pelfrey and Kevin Correia and trading for Worley, to go alongside Scott Diamond and a fifth starter, currently Pedro Hernandez. This season will look a lot different for the Twins if all the newcomers pitch like they have in the past.

That’s why Sunday felt so important. The Twins entered the day with a 5.01 ERA from their starting pitchers, ranking 27th in the majors and ahead of only three last-place teams: Toronto, San Diego and Houston. Their bullpen has been the American League’s best, but the Twins aren’t even a .500 team at the moment, in part because Worley (a 7.22 ERA) and Pelfrey (7.66 entering Sunday) have disappointed.