MILWAUKEE -- Brandon Woodruff and the Brewers have matched a streak of stout starting pitching established by Zack Greinke, Yovani Gallardo & Co. a decade ago.

On a testy night at American Family Field, it wasn’t enough.

Woodruff took a no-decision for the third time in as many starts after Brewers reliever Brent Suter served up a go-ahead home run to Cubs catcher -- and lightning rod -- Willson Contreras, who smashed a go-ahead home run in the eighth inning to send Milwaukee to a 3-2 loss on Tuesday and shushed the crowd while he circled the bases.

“We get it. There's a little rivalry,” Woodruff said. “But that's what makes these games fun. So yeah, it seems like every time we play these guys it's always going to be a close game and anything can happen.”

Woodruff did his part against the Cubs for the second time in six days, pitching six innings of one-run ball for the Brewers’ seventh consecutive start of at least five innings with no more than one run. It’s a modest threshold, no doubt, but it implies keeping the team in every game, and it’s easier said than done. Brewers starters hadn’t met those criteria in seven straight games since 2011, the year they emptied the farm system to acquire Greinke and Shaun Marcum in trades, and posted the National League’s best ERA.

Luis Urías had provided Woodruff a lead with a two-run home run in the second inning, so it was up to the Brewers’ bullpen to hold a one-run advantage over the final three innings. Brad Boxberger pitched a scoreless seventh inning but Suter faltered in the eighth against Contreras, who was hit by a pitch for the third time in five games between these two teams over the past nine days, then was behind the plate when Cubs reliever Ryan Tepera fired a 95 mph fastball behind Woodruff’s legs while the Brewers' starter was batting in the fifth.

Woodruff kept his cool and delivered a scoreless sixth. He handed the bullpen a 2-1 lead.

"I was fighting my delivery the whole night,” Woodruff said. “I just didn't have a good rhythm and was fighting the in-between tempo for me. I just couldn't really find it all night. But tonight was one of those grinded-out outings. Kind of had to bear down a little bit there. ... So, I was happy to get through six and put the team in a good position when I came out."

That’s been the story of the Brewers’ season so far: Solid starting pitching and an on again, off again offense. With Woodruff’s outing the ERA of Brewers starters is 1.94, best in the Majors by a relatively wide margin. Cleveland is second at 2.43 after Shane Bieber’s complete-game shutout against the White Sox on Tuesday.

The Brewers have had only one pitcher complete seven innings so far this season -- Woodruff last week against the Cubs at Wrigley Field, when he was working on a no-hitter after six innings. But they have nonetheless been baseball’s stingiest unit, with Woodruff and Corbin Burnes leading the way. Burnes is scheduled to start Wednesday’s series finale against the Cubs.

“It’s incredible. They’re doing their jobs every time and then some,” said Suter of the Brewers’ starters. “It's crazy, one or zero runs -- so kudos to them. I'm so proud of all of them, their development and everything, with such confidence. We have a lot of trust in every one of them.

“Now it's up to the bullpen to hold on to these leads. Unfortunately tonight, it was my fault. I mean, it happens, but it's really just a terrible feeling. I cost Woody the game, cost our team the game. It's just not a good feeling.”

Why Suter in that spot? The Brewers decided this week that their usual set-up man, Devin Williams, needed more regular work, so they pitched him Monday night in a lower-leverage spot. Manager Craig Counsell’s choices in the eighth included a second inning of Boxberger (he threw 12 pitches in the seventh), rookie right-hander J.P. Feyereisen, left-hander Suter, or Josh Hader for six outs.

Since the Brewers rarely use Hader beyond one inning nowadays, especially this early in the season when pitchers are still building a foundation, the eighth belonged to Suter.

“That’s, obviously, [Williams’] inning if he is built up and everything,” Suter said. “I tried to fill in and didn’t get the job done. We’re looking forward to when Devin gets built up and everything. That’s his inning for sure.”