Aramis Ramirez gave the home team hope on Saturday with a game-tying, two-out, two-run home run in the eighth inning, but Minnesota won in the 11th when pinch-hitter Trevor Plouffe homered with two outs off Brewers reliever Manny Parra.
Twins closer Matt Capps pitched a 1-2-3 inning for the save.
"We're trying to stay positive as much as we can and try to come out of it," Hart said. "We still have a great club. We have plenty of good times ahead. We can get on a roll, it just ain't there yet. We have a club that can go 20-5, but right now we're worried about trying to win a series."
That bid will have to begin on Monday against the Giants. On Sunday, the Brewers must win to avoid becoming the first team to be swept in a three-game series by the 14-26 Twins. More than a quarter of the Brewers' 162-game regular season will be in the books by Sunday night.
"I don't think there's really an explanation for it," said catcher Jonathan Lucroy, who stayed hot with an RBI single in the fourth inning. "We're just battling. Yeah, we're struggling, but the measure of a man is how your fight during tough times. That's all you can do it go out there and fight. This is our job. This is what we were born to do."
For the second straight day, this was a team loss.
In the field, the Brewers committed two more errors after being charged with four on Friday night. Hart dropped a fly ball in foul ground and in the sixth, a Rickie Weeks throwing error contributed to a crucial unearned run against Brewers starter Yovani Gallardo.
On the mound, reliever Juan Perez received a morning promotion from Triple-A Nashville and had a forgettable Brewers debut. He walked the first man he faced in the seventh inning to load the bases, then hit Ben Revere with an 0-and-2 pitch to force home a run that gave the Twins a 3-2 lead.
And at the plate, the Brewers struck out 14 times while drawing one walk -- an intentional one. Weeks was 0-for-5 with four strikeouts and saw his average fall to .154. The bottom four spots in the Brewers' order combined to go 0-for-18 with nine strikeouts.
"If we score runs, we're not talking about our bullpen," Brewers manager Ron Roenicke said. "That's the problem. We did a great job with Aramis coming back with a homer to tie it, and then we don't do anything for three innings. That gives the team a lot of chances to score. We need to be the team that does that."
Ramirez's homer in the eighth inning was his third home run this season and his first since April 28. It was also his first at Miller Park since the Brewers signed him to a three-year deal in December.
"Both sides threw just about everything we had out there," Twins manager Ron Gardenhire said. "Lots of back and forth. We had a lot of opportunities to get a big hit. I don't know how many we left on base but it seemed like an awful lot. But it was a good pitching performance from both sides."
Gallardo and Twins starter Carl Pavano kept the hitters mostly at bay over the game's first six innings.
Gallardo allowed two runs, one earned, on only three hits. But he walked three batters and labored in a 35-pitch fourth inning and a 22-pitch sixth that saw the Twins score a run in each on Brian Dozier sacrifice flies.
The Brewers also scored runs in the fourth and sixth innings against Pavano on RBI singles by Lucroy and Ryan Braun.
Lucroy improved his Major League-leading batting average with runners in scoring position to .560 (14-for-25), and was intentionally walked two innings later in a similar situation. Braun leads the Brewers with 24 RBIs.
But Weeks remained stuck in neutral. The slumping second baseman had a chance to impact the game with two on and two outs and the score still tied at 2 in the sixth, after the Twins intentionally walked Lucroy. But Weeks flew out to center field to end the threat.
"When your team's struggling, you're putting more pressure on each person," Hart said. "It's kind of natural. But when things aren't going our way, it's definitely escalating, where everybody is trying a little harder, trying to do too much."