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MILWAUKEE -- Jonathan Lucroy's first time as a cleanup hitter for the Milwaukee Brewers was a big success.

Lucroy homered twice and had a career-high seven RBIs, Zack Greinke pitched six strong innings to improve to 14-0 at Miller Park, and the Brewers beat the Minnesota Twins 16-4 on Sunday.

Lucroy connected on an 0-2 pitch from Jeff Gray in the seventh inning for his first career grand slam. The ball nipped the back edge of the padding in right before falling into the Twins' bullpen. A curtain call followed for the Brewers' catcher, who also had a solo homer in the first and an RBI single in the second.

"Coming up through high school, college and the minor leagues, I was a (No.) 3-, 4-hitter," Lucroy said. "I'm comfortable with it. I've been there before."

Lucroy's opportunities to bat cleanup were limited until this year. Ryan Braun and Prince Fielder held down the Nos. 3 and 4 spots, respectively, in the Brewers' lineup the previous two seasons. But, with Fielder gone, the offense sputtering and plagued by inconsistency, manager Ron Roenicke turned to Lucroy.

"When I got here, obviously with someone like Prince Fielder and Ryan Braun in (Nos.) 3-4, you're not going to be in there," he said. "If he calls me to be there, I'll be there. If not, whatever."

Lucroy came in batting a team-high .330 and was second behind Braun in RBIs with 20. Lucroy's performance Sunday elevated his average to .342 and gave him 27 RBIs, just one fewer than Braun's total.

"I'm just happy to help my team win any way I can," Lucroy said. "I'm just trying to have good ABs and hit the ball hard somewhere."

Despite the success, Roenicke said Lucroy will drop back into his regular spots in the bottom third of the order. However, if Lucroy continues blistering the ball, that might change.

"He'll go back to where he was," Roenicke said, but then added, "I hope he stays this hot so we have to make that decision."

While Lucroy seemed to be pounding the ball everywhere, Greinke was keeping the Twins from doing the same.

"He's nasty, though. Isn't he?" Lucroy said. "He's a lot of fun to catch, working his magic out there. Whenever this guy locates down and away, painting and with velocity and bite on his slider, mixing the slow curve ball, the changeup. This guy won a Cy Young, and there's a reason why."

Greinke (5-1) benefited from Milwaukee's season highs for hits and runs to extend his unbeaten streak to 20 starts as a Brewer at Miller Park. He allowed one run on five hits, struck out six and walked one.

Staked to a seven-run lead early, he allowed just one run on four hits through six innings. In the seventh, Trevor Plouffe singled with one out. Second baseman Edwin Maysonet's two-base throwing error put runners at second and third. After Denard Span walked to load the bases, Juan Perez relieved and struck out Ben Revere to end the threat.

With the victory, the Brewers avoided being swept in a three-game series with Minnesota for the first time since Sept. 15-17, 1978, when Milwaukee was still in the American League.

Braun went 3 for 4 with two doubles, a single, four RBIs and two runs scored. Corey Hart also had three hits, including his ninth home run of the season.

In the fourth, Braun's RBI double and Taylor Green's sacrifice fly pushed the lead to 10-1. An inning later, Braun made it 11-1 with a bloop RBI single.

Norichika Aoki pinch hit for Braun in the seventh and drove in a run.

The Brewers chased Jason Marquis (2-4) with a big six-hit, six-run second inning. Braun doubled in two, Lucroy had a bloop two-run single, and Hart and Travis Ishikawa each added run-scoring singles. Marquis also hit one of the 10 batters he faced in his shortest start of the season.

After Ishikawa's two-out RBI hit, Anthony Swarzak took over for Marquis and retired Cesar Izturis on a fly ball.

"I'm putting the team in a hole every time I step on the mound," Marquis said after losing his fourth straight start. "I can't get it right right now. They hit good pitches and bad pitches."

Marquis' last victory was April 29, when he beat Kansas City.

Hart led off the bottom of the first with a solo shot that nearly cleared the second tier of seats in left. Lucroy followed two outs later with another solo blast. It landed in the same tier in left, but just a few rows in.

The Twins' bright spot was Revere, who kept up his strong hitting since being recalled May 17. He doubled and scored on Josh Willingham's single in the Twins' first. Revere came into the game batting .400 with two runs scored and two stolen bases.

Brian Dozier had a RBI single in the eighth for the Twins.

Minnesota scored a run in the ninth when Izturis couldn't field Darin Mastroianni's two-out roller to short with the bases loaded. Then reliever Kameron Loe walked in a run before retiring Dozier to end the game.

The huge lead gave Roenicke a chance to move Hart to first to start the seventh. With Mat Gamel (right knee) out for the season, Ishikawa became the starting first baseman. While Green can play there, Roenicke sees Hart as a more long-term option. Plus, with Hart at first, an outfield position opens up that would allow Carlos Gomez. Nyjer Morgan and Aoki to see more playing time.

Game notes

C Drew Butera drew a walk as a pinch-hitter in the eighth and stayed in the game as the Twins' fifth reliever. He pitched a scoreless eighth. ... Hart's home run in the first traveled an estimated 455 feet while Lucroy's went 405 feet. ... The Brewers reinstated OF Carlos Gomez from the 15-day disabled list Sunday. They had optioned INF Brooks Conrad to Triple-A Nashville after Saturday's game. ... Brewers reliever Tim Dillard was ejected by home plate umpire Hunter Wendelstedt in the ninth for throwing behind Minnesota's Jamey Carroll. "I heard Lucroy say, 'Nyjer Morgan," Carroll said, "but, we got our conversation cut off by Hunter. I wasn't expecting anything."