Morneau hit a two-run homer in the first and a three-run shot in the fourth, while drawing a walk in between. Morneau was due to lead off the fifth inning, but Rene Rivera replaced him as a pinch hitter.
"I've been feeling better every day, especially the last three or four days," Morneau said. "I've been taking a lot of swings and the timing is starting to feel a lot better. The swing is starting to feel a lot better. Home runs happen.
"It's not going to be a day like that every day, but you have good days, and it's good to have one of those days now and get the confidence going. Hopefully we continue it and keep swinging the bat."
Morneau, who also doubled against the Yankees on Friday, hasn't played first base since March 13, and there remains a chance he could start the season as the club's designated hitter.
But Twins general manager Terry Ryan said that Morneau is simply serving as DH because it gives him more at-bats and that the club isn't worried about his defense. Even after Morneau's big game on Saturday, he's hitting just .154 with three extra-base hits.
With Morneau serving as DH, Joe Mauer made his third start of the spring at first base while Chris Parmelee started in right field for the first time after playing three innings there on Friday.
Although Parmelee only played first base in his 21-game stint with the Twins last season, he's no stranger to right field, as he's played there 282 times in the Minors, compared to 323 games at first base.
Parmelee, who hit .355 with 10 extra-base hits as a September call-up last year, has carried that over into the spring, as he also homered on Saturday and is hitting .316 with three homers, a double and a triple this spring.
Ryan said there remains a chance that Parmelee could make the club, which means Morneau would start the season as DH.
"He could DH," Ryan said. "We'll have to see how it plays out this spring. Right now, Parmelee is having quite a spring. You start to say, 'Jeez, how are we going to get that bat in the lineup?' He's a first baseman and an outfielder. He can play both."
Morneau said he'd like to play first base a few more times this spring, and while he'd rather serve as the club's first baseman, he's OK being relegated to DH duty if it helps the club.
"If it's what keeps everybody in the lineup, and if it's what I have to do, it's what I have to do," Morneau said. "But I don't think we've made a decision on that. We'll cross that bridge in about two weeks."