Morneau's big hit came off Baltimore closer Jim Johnson with two out. It scored Aaron Hicks, who reached on an error by first baseman Chris Davis and advanced to second on a two-out walk from Josh Willingham.
"It was just fun to get on the board and start filling up those columns, but I'm still 15 RBIs behind [Orioles slugger Chris] Davis," Morneau said with a laugh. "It was a good win for us. The job [Josh] Roenicke did throwing the ball gave us a chance. And then we took advantage of an error late in the game, and so it was nice to be on the right side of that game."
Morneau had to be reminded that he's actually 16 RBIs behind Davis, who leads the Majors with 17 after picking up one on a bloop single in the fifth.
But the Twins kept Davis from homering for the first time this season, and Morneau said he'll take his one RBI, as it came off one of baseball's best closers from a year ago and improved the Twins to 3-2 on the season.
Morneau sent a 2-1 changeup from Johnson back up the middle, and Hicks scored his first big league run.
"It was a pretty good pitch to hit right over the plate," said Morneau, who is hitting .389 thus far. "I just tried to keep it simple and put a good swing on it and take my chances. So it's nice to get those and get the confidence going."
It made a winner out of Roenicke, who tossed three scoreless innings after taking over for starter Vance Worley. Closer Glen Perkins threw a scoreless ninth to pick up his first save of the season.
"Roenicke was a big story for us," Twins manager Ron Gardenhire said. "What a super job. He threw some big innings. That was a big performance from him because we knew our bullpen was beat up."
Worley didn't factor into the decision after he labored through five innings. The right-hander gave up five runs -- four earned -- on 10 hits and a walk.
"I made some mistakes up in the zone and toward the end," Worley said. "It's how all the runs came in."
The Orioles took an early lead against Worley, scoring twice in the first inning. With runners on second and third, Adam Jones hit a soft tapper back to Worley, who threw to first, despite not having a play. Morneau couldn't hold on to the throw, which allowed both runs to score.
The Twins came back with a run in the second on a sacrifice fly from Brian Dozier before adding four runs in the third inning against Orioles starter Chris Tillman. Ryan Doumit brought home the first run with an RBI single before Trevor Plouffe plated another with a sacrifice fly. Chris Parmelee then blasted a two-run homer on a 3-0 fastball from Tillman for his first long ball of the year.
"I had the green light, and it was a pitch I could drive," said Parmelee, who also made a sliding catch in right field in the ninth. "So I just let it go."
But the lead didn't last long, with the Orioles scoring in the third on a bloop RBI single from Davis and two more in the fifth on a two-run single back up the middle by Jones with the bases loaded. Davis went 1-for-3, and while his home run streak ended at four games, he can tie a club record for consecutive games with RBIs on Sunday if he drives in another run.
"I wasn't actually thinking I need to hit a homer," Davis said. "My mindset was more 'Drive in runs.' Homers come and go, they come in bunches. On a cool night, the ball Parmelee hit was absolutely murdered. It was really the ball I thought that was a no-doubter."
It was a nice bounce-back win for the Twins, who were leading late against the Orioles on Friday only to see Davis hit a go-ahead grand slam in the eighth inning.
"We feel like we can play with anybody," Gardenhire said. "Tonight was a good win for us just to get back on the right track."