Bassitt (5-4), who entered with a 7.62 ERA in his last five starts, allowed just three singles and one walk with seven strikeouts. He got the Brewers to hit into double plays immediately after each of their hits, including in the sixth when Milwaukee had runners at the corners before Willy Adames grounded into an inning-ending double play.
Bassitt, who had a 2.61 ERA in his first five starts working with James McCann, said he spent a lot of time between starts with catcher Tomas Nido, who took over as the team's top backstop after McCann went on the injured list May 13.
''This is 100% all on me: I just thought me and Nido - we weren't on the same page at all,'' Bassitt said. ''The more and more I fought, the worse and worse I did. So we just spent the last week just getting to know each other and better in the game.''
It was the third time Bassitt has thrown eight scoreless innings and the first since his lone shutout, a two-hitter for Oakland against the Los Angeles Angels on May 27, 2021.
''Guys like him, you just trust the moxie and the want to they have and they figure it out and make the adjustments,'' Mets manager Buck Showalter said.
Drew Smith worked a perfect ninth to complete New York's 10th shutout of the season.
Milwaukee has dropped nine of 10, getting shut out four times during that span.
''Yeah, we're in a little bit of a funk, but every team is going to go through that. Everybody's going to have their little stretches, might as well get it out (of) the way earlier than later,'' Brewers first baseman Rowdy Tellez said. ''It's just one of those things right now where we're trying to roll with the punches.''
The Mets produced all the offense they'd need against Adrian Houser (3-7) in the first. Brandon Nimmo led off with a double but stayed at second when Starling Marte beat out an infield single. Both runners moved up a base on Francisco Lindor's groundout before Nimmo scored on Alonso's single.
Jeff McNeil followed by swinging on 3-0 and hitting a comebacker that glanced off the glove of Houser. Adames, the shortstop playing on the second base side in the shift, couldn't adjust to the redirection and the ball skittered into right field as Marte scored. Alonso stayed at third as McNeil slid into second with a double.
''He threw a pretty good 3-0 pitch - started middle, went away from me and didn't put a great swing on it. But that's baseball, you get lucky sometimes,'' McNeil said.
Eduardo Escobar followed with a sacrifice fly.
''You can't put any pressure on the defense if you don't put it in play,'' Showalter said. ''That's kind of been a lot of our guys' mantra. And that was a great baserunning play by Mac. A lot of guys are satisfied with (a single).''
The Mets extended the lead in the fifth, when Nimmo and Marte led off with singles before Nimmo scored on a one-out single by Alonso - his National League-leading 59th RBI.
Houser allowed four runs on eight hits and one walk with three strikeouts in 4 2/3 innings for the Brewers. He threw 37 of his 96 pitches in the first.
''He battled well through the inning, but they made him throw a ton of pitches. He didn't pitch poorly that inning, necessarily,'' Brewers manager Craig Counsell said. ''He had maybe too many misses that kind of led him into some deep counts, but came back and pitched pretty well. That line score could have looked a lot different, I thought.''
The Brewers, whose pitching staff has been wracked by injuries, claimed right-hander Chi Chi Gonzalez off waivers from Minnesota.
Counsell said Gonzalez, who is expected to join the team Wednesday, could be utilized as a starter or long reliever. Brewers starters Brandon Woodruff (ankle, Raynaud's syndrome) and Freddy Peralta (right shoulder) are on the injured list along with six relievers.
Gonzalez is 9-23 with a 5.69 ERA in six big league seasons dating to 2015. He had a 7.71 ERA in two starts for the Twins, who designated him for assignment Saturday.
To make room for Gonzalez on the 40-man roster, the Brewers shifted Peralta to the 60-day injured list.
Brewers: Woodruff, dealing with numbness in his three middle fingers due to Raynaud's syndrome, only threw fastballs during his bullpen. Counsell said Woodruff appears to be making ''small progress every day.'' . INF Luis Urias returned to the lineup and went 0 for 3 after exiting Sunday's game with a tight right hamstring. . 2B Kolten Wong (right calf), who hasn't played since June 7, participated in pregame work with his teammates.
Mets: RHP Jacob deGrom (stress reaction on his right scapula) threw a 30-pitch bullpen and is slated for an ''up-and-down'' bullpen session Friday. . RHP Max Scherzer (left oblique) threw in the outfield and is expected to throw a simulated game Thursday. . RHP Trevor May (right triceps inflammation) planned to throw Tuesday, continuing an every-other-day progression that began Friday. . RHP Colin Holderman (right shoulder impingement) is week-to-week after undergoing an MRI.
Brewers: RHP Corbin Burnes (3-4, 2.48 ERA), the reigning NL Cy Young Award winner, is 0-2 with a 6.75 ERA in two starts this month.
Mets: LHP David Peterson (3-0, 3.00 ERA), who had his previous turn in the rotation skipped, hasn't lasted more than 4 2/3 innings since May 23.
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