MILWAUKEE -- Corbin Burnes tied a Brewers strikeout record on Sunday, but he would have rather had some run support. 

After scoring 20 runs and hitting nine homers while running away with the first two games of the series, the Brewers’ bats fell silent against Marcus Stroman and the Cubs in Sunday’s finale at American Family Field, a 2-0 Milwaukee loss that continued a bad habit of giving Burnes little support.

The Brewers have scored nine runs with Burnes on the mound during his first five starts this season. His 2.48 runs of support per nine innings ranks 10th-lowest among Major League qualifiers -- and fifth-lowest in the NL.

“You can’t put your finger on it,” said outfielder Andrew McCutchen, who went 0-for-4 and struck out to end the game. “I remember watching [Jacob] deGrom go out there every day and not have any support any time we faced him. Sometimes, it just happens to be that way. It’s part of it sometimes. It’s not like we’re sitting around having a meeting about it. Sometimes it just happens like that.

“Sometimes it’s a crazy game we play. You just have to show up and get them the next game.”

Burnes deserved better on a day when he didn’t allow a baserunner until the fifth inning and became the second pitcher in franchise history to reach double-digit strikeouts in three straight starts. With 31 strikeouts over his last three starts against the Pirates, Giants and Cubs, Burnes wrote his name in the club record book alongside Yovani Gallardo, who struck out 12, 13 and 11 batters in his final three regular-season starts in 2011.

Over his last four starts, Burnes has allowed four earned runs on 13 hits with four walks and 39 strikeouts in 27 2/3 innings.

“That guy's incredible, man,” said Stroman. “He's one of the very few pitchers I watch video on, and really kind of dive into on his stuff, his sequencing, his tunneling. I think he's incredible with his pitch mix. Anytime you're going up against that guy, you know you have to bring your 'A' game.”

That’s what Stroman did, allowing two Brewers hits in seven scoreless innings. Burnes, meanwhile, allowed two runs on four hits in seven innings -- but rued two mistakes.

One was a “sinker that didn’t sink” in the fifth inning, which Patrick Wisdom crushed for a home run to abruptly end Burnes’ 13-up, 13-down start to the game. The other was a “bad curveball” in the fifth, when Seiya Suzuki made it 2-0 with a double into the left-field corner.

“The two pitches he gave them that they had to hit,” Brewers manager Craig Counsell said, “they did something with it.”

“That lead, [with] the way Stro was throwing, was a big sigh of like, 'OK, we've got this thing, if Stro stays on par, we've got a fully-loaded bullpen,'” Cubs manager Cavid Ross said. “Stro just took the bull by the horns, so to speak, and took us all the way to the eighth.”

Before the Cubs grabbed their lead, Burnes was as efficient as it gets. He needed nine pitches in the first inning, 11 in the second, 11 in the third and nine in the fourth before Wisdom finally got him during a 15-pitch fifth. It was in the sixth that Burnes began to wobble. He needed 27 pitches for that inning alone.

“That’s my goal every time out there: Attack early and attack often,” Burnes said of the early efficiency. “It’s quick punchouts or balls in play. So that’s kind of to a T of how I want to go for the first five innings. Then, the next two, I just threw way too many pitches.”

Stroman had no such trouble. Not only did the Brewers fail to score, they barely threatened against Stroman and relievers Rowan Wick and David Robertson.

Only one Milwaukee runner reached scoring position -- Tyrone Taylor, after a one-out double in the third.

“They just played better in all aspects of the game and beat us,” Burnes said.