Baker's strong outing and Nick Blackburn's new contract was tempered by closer Joe Nathan returning to Minnesota for tests on his surgically repaired right elbow. The All-Star right-hander felt discomfort after throwing 20 pitches against the Red Sox on Saturday.
"It wasn't anything that was too severe," Nathan said. "Right now, it's just a matter of gathering information and treating it the best way we can until we get that information. I think everyone is optimistic that it's just something from the post-op. Scar tissue or something like that. I'm going to treat it that way until I'm told otherwise."
The 35-year-old Nathan had surgery Oct. 20 to remove bone spurs from his elbow. He went 2-2 with a 2.10 ERA and a career-high 47 saves last year.
Blackburn got a $14 million, four-year deal similar to the one Baker signed last year. Blackburn's contract includes an $8 million club option for 2014.
"The security part is great," said Blackburn, a 29th-round draft pick in 2001. "A few years ago, I didn't think I'd be in this position. I was thrilled that they made the offer, and I couldn't wait to sign it.
"I'm not going out there having to prove anything. I'm just working on throwing the ball over the plate and getting some ground balls. I don't have to worry about anything anymore. I can just focus on pitching."
Blackburn posted almost identical seasons in the past two years. He was 11-11 in 33 starts in 2008 and 2009. He had a 4.05 ERA two years ago and a 4.03 ERA last season.
"We went into the winter, we tried to identify players who might be a good fit for multiyear contracts," general manager Bill Smith said. "He's had two remarkably consistent seasons. He pitched a lot of big games for us over the past two years."
Baker, who signed a $15.25 million, four-year contract last year, gave up three hits, struck out two and walked none against New York.
"It went well," Baker said. "We wanted to establish the fastball down and away. I threw a few breaking balls. I did well. I'm just trying to mix pitches."
With Nathan's health in question, the Twins at least had solid results from their regular relievers. Matt Guerrier, Jon Rauch, Jesse Crain and Pat Neshek combined for three strikeouts and one walk in five innings of four-hit ball.
Sergio Mitre, a long shot for the fifth spot in New York's rotation, worked three scoreless innings. He struck out three, walked one and allowed two hits.
"I think my first one was pretty good, and this one was pretty good," Mitre said. "A couple more to go, and we'll see where we stand."
Chad Gaudin, also a long shot for New York's rotation, didn't fare as well as Mitre. Gaudin gave up three runs and three hits in two-plus innings.
Juan Portes hit a grand slam and a two-run homer, and Brock Peterson also went deep for the Twins.