Youkilis collected another RBI with a sixth-inning sacrifice fly, driving home Brett Gardner, and Kuroda continued to hone his breaking pitches to give the Yankees another reason to feel confident about their starting pitching.
The veteran right-hander limited St. Louis to three hits over four scoreless innings, walking none and striking out six. Kuroda threw 38 of 62 pitches for strikes in his second start of the spring.
"Obviously I'm not at peak of my conditions, but I'm in a good place," Kuroda said through an interpreter.
David Robertson, who had been sidelined since March 7 with stiffness in his pitching shoulder, hurled a scoreless sixth inning for New York.
Other than the pitch to Youkilis, Lynn provided a solid outing in his third start of the spring. The right-hander permitted two hits with a walk and a strikeout, throwing 44 of 68 pitches for strikes.
"You go out there every day to try to fine tune," Lynn said. "I just wanted to make sure I threw all my pitches and try to get ahead. I didn't have the best success at that, but I was able to make the pitches later in the count to get the ground ball and things like that. I felt pretty good."
The Yankees added two runs in the seventh, as Seth Maness hit Matt Diaz to force home a run and Zoilo Almonte worked a bases-loaded walk facing Victor Marte.
Up next: The Yankees hit the highway on Tuesday to visit the Rays in Port Charlotte for a 1:05 p.m. ET contest. Ivan Nova gets the ball for his third start of the spring, with Alex Cobb on the mound for Tampa Bay. The Yankees' travel roster will be highlighted by Travis Hafner, Francisco Cervelli and Eduardo Nunez.
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.