MILWAUKEE — The way Max Scherzer was pitching, the Milwaukee Brewers were going to need a bit of luck to even manage getting anyone on base.

They got it — barely.

Scherzer struck out a Nationals-record 16 and threw a one-hitter, losing his perfect-game bid on Carlos Gomez’s broken-bat, bloop single in the seventh inning as Washington beat the Brewers 4-0 Sunday.

“I was able to execute every pitch for the most part where I wanted to,” Scherzer said.

Gomez opened the seventh with a looper to shallow right field that just fell inches beyond the outstretched glove of second baseman Anthony Rendon. Gomez, indeed, said he “got lucky” to get that hit off Scherzer.

“I wouldn’t imagine that that’s going to be the last opportunity that he’s going to have to do something special,” Nationals manager Matt Williams said.

Scherzer watched the ball drop, then turned away.

“Why would I be disappointed on a broken-bat base hit? It takes luck to do that,” Scherzer said.

Scherzer set a career high for strikeouts and broke the Nationals mark of 14 set by Stephen Strasburg in his big league debut in 2010. The franchise record of 18 was set by Bill Gullickson in 1980 with Montreal — the Expos moved to Washington for the 2005 season.

Scherzer (7-5) walked one and finished the day with a 1.93 ERA.

He was still throwing fastballs in the mid-90s mph in the eighth inning. Scherzer’s off-speed stuff kept hitter off-balance.

“Every at-bat you stand at the plate, you see him ... throwing a pitch consistently, throwing the ball where the catcher wanted the ball, pounding the strike zone down,” Gomez said. “And he got that change and the slider all day long.”

Scherzer, in the first season of a $210 million, seven-year contract, threw his second complete game.