Instead, the brand new papa took the mound and delivered the best start of his young career, pitching the Twins back into first place in the AL Central, a half-game ahead of Chicago.
Perkins allowed four hits and three walks over eight outstanding innings and light-hitting Adam Everett had a two-run homer, lifting Minnesota to a 4-0 victory over the reeling Yankees.
"It's a great feeling," Perkins said. "I always pitch for my family. That's why I'm playing, to help support them.
"You're tired and you're all those things, but to be able to do that a day after having a baby is really special. You get a little bit extra when you're in a situation like that."
Perkins (9-3) struck out four and induced two inning-ending double plays, receiving a standing ovation when he left after the eighth.
"You just don't know how a young pitcher is going to react, but he looked pretty calm when he walked to the mound," said Twins manager Ron Gardenhire, who got career win No. 600.
Joe Nathan fanned Bobby Abreu, Alex Rodriguez and Xavier Nady in the ninth to complete the first shutout of the Yankees at the Metrodome since June 24, 1996.
It's difficult to say which was more unlikely - the 25-year-old Perkins keeping the veteran Yankees hitters on ice less than 24 hours after being in the hospital with his wife for the birth of their second daughter, or Everett hitting his first homer since May 11.
Either way, they both helped the Twins extend the Yankees' losing streak to a season-long four games, and push New York a little further down the totem pole in the playoff race.
The Yankees (63-56) dropped five games behind Boston, which leads the wild-card standings. New York is nine games back of first-place Tampa Bay in the AL East and is starting to get asked about possibly missing the playoffs for the first time since 1993.
"The problem is we're not winning. Not the teams in front of us," manager Joe Girardi said. "Nothing says we can't turn things around and win eight in a row. It's happened before and I don't see why it couldn't happen again."
Former Twin Sidney Ponson (7-3) gave up four runs and seven hits in 7 2-3 innings, just his second loss for the Yankees after starting the season with Texas. His biggest mistake came to Everett, a 31-year-old shortstop with shoulder problems who was hitting .209 at the start of the day.
His homer landed just beyond the glove of a leaping Justin Christian and fell into the second row of seats in left field, giving the Twins a 2-0 lead in the second inning.
"I pitched good enough to give us a chance to win, but with two outs I walked the third baseman and hung a pitch," Ponson said. "I'm not too happy with it."
Perkins took over from there.
He wasn't even sure he was going to be able to make the start when he hopped a 7 a.m. flight from Kansas City on Sunday to be with his wife, Alisha.
Lyla Cynthia Perkins was born about 6 p.m. on Sunday in St. Paul.
"Playing major league baseball, playing against the Yankees, it doesn't matter what kind of sleep you get," he said. "There's plenty of adrenaline and I definitely used that to my advantage tonight."
The Yankees managed only one runner past first base, when Robinson Cano advanced to third after Perkins threw a pickoff attempt past first baseman Justin Morneau for a second-inning error.
But the lefty settled down and got Melky Cabrera to ground into a double play, ending New York's only threat of the night.
"It's frustrating," said Derek Jeter, who went 0-for-4. "We've got to get rolling offensively. That's the bottom line. We have to turn things around quick."
Notes: Yankees CF Johnny Damon had the night off. Girardi said Damon will play in the final two games of the series. ... Nathan announced a gift of $500,000 to his alma mater, Stony Brook University in New York, to build a new baseball field that will be called Joe Nathan Field.