The Twins' right-hander allowed two hits over seven innings to lift Minnesota to a 2-0 victory and a split of the doubleheader on Wednesday.
In the first game, the Red Sox left-hander allowed one run and two hits in seven innings in a 6-3 win.
"You kind of count on your veterans over the long haul," Twins manager Paul Molitor said, "but when young guys can step in and play a part in what kind of season unfolds for your club, it's a huge lift."
May struck out nine and walked none. He has issued one walk with 26 strikeouts in 26 2/3 innings over his last four starts.
"If I'm going to get beat I'm going to make the other team beat me," he said.
Glen Perkins pitched the ninth for his major league-leading 20th save in as many chances.
Boston's Rick Porcello (4-5) rebounded from two starts in which he gave up 13 runs in 11 1/3 innings. On Wednesday night, he allowed two runs and five hits with five strikeouts and no walks in eight innings but still took the loss.
"He got better as the night went along," Red Sox manager John Farrell said. ""We just couldn't get anything going offensively."
In the opener, Rodriguez followed his major league debut with another outstanding performance. He became the first pitcher since at least 1900 to pitch at least seven innings, allow no more than three hits and no more than one run in each of his first two outings.
"He's a pleasure to watch," Farrell said, "a special kid."
Obtained from Baltimore for reliever Andrew Miller at last year's trade deadline, Rodriguez (2-0) made his debut seven days ago in a 5-1 win at Texas that he left after giving up three hits in 7 2/3 shutout innings.
He was surprised last year when the Orioles traded him, he said, "but look at where I am right now. Now I'm going to say thanks to them."
Farrell is thankful to have Rodriguez in Boston's struggling rotation and has no plans to send him back to Boston's Triple-A team in Rhode Island.
"If he goes to Pawtucket," Farrell said with a smile, "it's only on the way to Baltimore" where Boston starts a trip Monday.
The opener was a makeup for Monday night's rainout.
"It's not very fun when you feel like you're just constantly trying to battle out of jams," Hughes said.
After going 1-6 on a road trip, Boston got its second outstanding pitching performance against Minnesota. Clay Buchholz allowed three hits in eight innings in a 1-0 series-opening win Tuesday night.
"Everybody's throwing the ball well," Porcello said. "We need to keep doing that to provide some support for our offense."
Rosario has hit safely in eight straight games and Torrii Hunter has reached base in 12 in a row.
Red Sox President Larry Lucchino and general manager Ben Cherington picked up trash in the stands between games.
Twins: RHP Ricky Nolasco is expected to throw Thursday after leaving Sunday's game against Toronto in the second inning with pain in his right ankle. He is not on the DL.
Red Sox: LHP Brian Johnson, a top prospect, was scratched from his Triple-A start Wednesday to get extra rest. In 10 starts with Pawtucket, he is 6-3 with a 2.60 ERA. "There's a typical approach taken with all starters there where they'll skip a start at some point," Farrell said.
Twins: LHP Tommy Milone (2-1) pitches in the finale of the four-game series Thursday night, his first appearance for Minnesota since being sent to Triple-A Rochester on May 1.
Red Sox: RHP Steven Wright (2-2) makes his fourth start this season in place of Justin Masterson, who is on the DL. In his last start, the knuckleballer allowed two homers to Josh Hamilton in a 7-4 loss at Texas.
- Home Plate Umpire - Mark Wegner
- First Base Umpire - Marty Foster
- Second Base Umpire - Mike Muchlinski
- Third Base Umpire - Ben May