Axford capped a strong effort by the Milwaukee bullpen with a strikeout of Morneau to end a game that saw the Brewers set a club record with five wild pitches.
Axford earned his sixth save and second in two nights. After Joe Mauer's RBI double with two outs, Morneau sharply yanked a slider down the right-field line foul, then looked at strike three.
"It's not like we were trying to do the same sequence by any means, we were just trying to stay away from his bat," the closer said of his second successful meeting with Morneau in as many days.
Manny Parra (2-5) won for the first time as a starter this season. He tied a 35-year team mark with four wild pitches, including one during an intentional walk. Reliever Kameron Loe threw a fifth to set the team record for wild pitches in a game, but the AL Central-leading Twins failed to take advantage.
"It was a disappointing night for us," Twins manager Ron Gardenhire said. "We had some opportunities, didn't get them in, but I think we gave them some."
Weeks had three hits, drove in three runs and scored twice.
"He can do a lot of things up there. He's more of a Rickey Henderson kind of guy because he can run, hit home runs and he's gotten better defensively," said Corey Hart, who drove in Weeks in the third inning to give Milwaukee a 1-0 lead. "He's a breath of fresh air right now."
Career saves leader Trevor Hoffman began warming up late in the eighth, but quickly sat back down when Milwaukee failed to add any more runs after Weeks' run-scoring single gave the Brewers a 5-2 lead.
None of the relievers' innings were easy in Milwaukee's third straight win.
Still, Axford stayed perfect by converting his sixth straight opportunity since taking the role from Hoffman. Brewers manager Ken Macha said Axford needs a day or two off after also converting a six-out save Tuesday night.
Milwaukee, now 2-0 to start a nine-game homestand, finally got the best of its border rival and snapped a streak of five straight series wins by the Twins.
"They've been wearing us out since I've been here," Hart said. "It's nice to get the series and hopefully tomorrow we can come out hot. It's just refreshing that we're playing good baseball and we feel like we're not out of it yet."
Minnesota starter Francisco Liriano (6-5) held the middle of Milwaukee's order of Prince Fielder, Ryan Braun and Casey McGehee to 0 for 9 with five strikeouts. It was the rest of the lineup that hurt him.
Parra won for the first time as a starter since Sept. 25, but it wasn't pretty.
"I think my Adrenalin, it was going so much, I threw that wild pitch," Parra said. "I didn't want to intentionally walk him anyway."
Good thing he didn't.
The throw allowed Jason Kubel to move to third with one out, but Parra went on to pitch to Young and forced him to hit a short chopper to McGehee at third, who threw out Kubel at the plate.
"It was really big. It was huge," Parra said. "[I] made some pitches when I had to."
And one more he didn't, firing a final wild pitch during a walk to Nick Punto.
He exited for Braddock, who struck out pinch-hitter Jim Thome, batting for Liriano, to end the inning and preserve Milwaukee's 3-2 lead.
"It feels good to get a win, it feels good for us to win another game and just start building momentum," Parra said. "This is a crucial 20 games right here for us. If we can make a little run and put ourselves in good position after the All-Star break, I think that's what we're trying to do."
Morneau is 13 of 23 this season with a .347 career average against Milwaukee, but is hitless with three strikeouts against Axford. ... Braun drove in Weeks with a fielder's choice in the seventh to make it 4-2. ... Ed Sprague also threw four wild pitches at Texas on May 14, 1975. ... Braddock returned after missing a game due to a death in the family. ... Brewers RHP LaTroy Hawkins (right shoulder) says he's nearing the end of his scheduled throwing program and expects to be on the mound to continue rehab next week.