Baker worked eight sharp innings for his best start of the season as the Twins beat the Orioles 6-1 in the nightcap.
In the opener, Nick Markakis drove in three of the five two-out runs off Liriano and Baltimore cruised to a 7-3 victory. The doubleheader made up for a rainout Friday night.
The two teams play the finale of their four-game series Sunday.
"We're in a position to win three out of four. I haven't been able to say that very often as of late," Orioles manager Dave Trembley said.
After starting 2-16, the Orioles have won seven of 13 and looked impressive against Liriano, April's American League pitcher of the month. Markakis, Adam Jones and Julio Lugo went a combined 7 for 14 with five RBIs against Liriano, but were 2 for 11 against Baker.
"I want to stay aggressive against a good-hitting team like this," Baker said. "You need to make good pitches early in the count, and that's the key. I was able to do that tonight."
Joe Mauer returned to the lineup in Game 2 for the first time since missing eight games with a bruised left heel. The reigning AL MVP drew a standing ovation as a pinch hitter in the eighth inning, but struck out with the bases loaded and the Twins leading 4-1.
Earlier in the day, Gardenhire had ruled out Mauer for the second game.
"The situation came up and you run him up there," the manager said. "It's pretty exciting, to tell you the truth, to run him up there and get that out of the way. He hadn't swung in a while."
Light-hitting Drew Butera followed Mauer with a two-run single, giving Baker (4-2) more than enough support. The Twins starter scattered three hits -- including a solo homer to Luke Scott in the fifth -- while winning for the first time since April 16.
"A good way to finish off a very, very long day," Gardenhire said.
Orioles starter Kevin Millwood (0-4) gave up three runs and seven hits over seven innings in Game 2, and dropped to 0-8 against Minnesota in 13 career starts.
"All in all for me to go out against those guys and give up three runs in seven innings, I don't feel great about it, but those guys to me are kind of like the '27 Yankees," Millwood said. "They beat me up pretty good. Baker threw a great game. What can you do?"
Jeremy Guthrie (1-4) fared much better in the opener, allowing five hits and three runs while pitching into the seventh inning for Baltimore. He also got more run support from his offense, thanks to a flurry of well-placed singles that knocked Liriano from the game.
"We finally got some hits to fall in," Trembley said. "The breaks went with us. We've hit some balls on the button and have had nothing to show for it. Today they didn't exactly look pretty, but they gave us good results."
Justin Morneau hit his first Target Field homer after going deep six times on the road, a two-run shot that gave the Twins a first-inning lead, but that was about all they could muster.
Markakis hit a two-run single with the bases loaded in the third on a roller up the middle that Liriano and shortstop Brendan Harris just missed. Three more runs scored on balls that found grass before gloves in the fourth, and the Orioles took a 5-2 lead.
"Sometimes those hits go your way. Sometimes they don't. It's a cliche, but it's a cliche for a reason," said Minnesota's Michael Cuddyer, who took Guthrie deep in the fourth and has five of his team's nine home runs in 15 home games.
Many of the Orioles' 10 hits were loops and bloops to the outfield, and a few of them barely eluded the infield dirt. Nolan Reimold's one-out single that started the rally in the third bounced high off third base and past Nick Punto's reach.
"You make a good pitch, and they still get a base hit," said Liriano, who had thrown 17 scoreless innings to start his experience at Minnesota's new ballpark. "There's nothing I can do about it."
The last doubleheader the Twins played at home was in 2007, the result of a rescheduling following the fatal freeway bridge collapse near downtown. Baker pitched the night game that time, too, and took a perfect game into the ninth inning. ... The Orioles hadn't played a doubleheader since the end of the 2008 season, a September twinbill against Tampa Bay.