The Mets went 2-for-13 with runners in scoring position and wasted a credible spot start by Nelson Figueroa (0-1), called up from the minors to pitch in place of No. 2 starter Mike Pelfrey (forearm tendinitis).
Coffey, who hasn't allowed a run since joining the Brewers last September, earned his first save since 2006 with Cincinnati.
The back end of Milwaukee's bullpen is in flux with career saves leader Trevor Hoffman on the disabled list, but Coffey keeps getting the job done.
Suppan hit a leadoff single in the fifth, moved to third on Rickie Weeks' ringing double and scored on Corey Hart's sacrifice fly to give Milwaukee a 2-1 lead.
Cameron, who played for the Mets from 2004-05, made it 3-1 with a shot to left-center in the sixth, his fourth of the season.
Omir Santos' leadoff triple in the seventh chased Suppan, and an infield single by Jose Reyes off Mitch Stetter cut it to 3-2. But Coffey came on with the bases loaded and one out to face slugger Carlos Delgado, who grounded into a 1-2-3 double play.
New York put its first two batters on in the eighth against Coffey, but Fernando Tatis struck out and Santos lined into an inning-ending double play.
Weeks provided an insurance run with a two-out RBI double in the ninth, giving him three hits. Coffey worked a one-hit ninth and pumped his first when David Wright hit a soft looper for the final out.
The burly right-hander has not allowed a run in 17 innings spanning 16 games since he was claimed off waivers by the Brewers last Sept. 10.
Suppan was charged with two runs and eight hits. He struck out four and walked one.
Milwaukee pitchers have delivered four straight quality starts, though a Brewers starter has yet to go seven innings this year.
Delgado's two-out RBI double put the Mets ahead in the first, but Suppan pitched out of trouble for much of the afternoon. He retired Gary Sheffield on a hard grounder with two on to end the inning, then induced a double-play grounder from Delgado to close the third.
New York failed to take advantage of a break in the fifth, when Hart lost Reyes' high fly in the sun - more evidence that right field can be awfully tricky at Citi Field. Reyes raced to third for a triple but was stranded when Daniel Murphy, who had three hits, grounded out.
Suppan got Tatis on a long fly to left with two on to end the sixth.
Hart singled to open the third, stole second and scored on Prince Fielder's groundout to tie the score 1-all.
Pitching for his hometown team, Figueroa allowed three runs and five hits in six innings.
The 34-year-old right-hander, who grew up a Mets fan in the Coney Island projects, had a storybook night against the Brewers at Shea Stadium last April. With a huge flock of family and friends in attendance - some watching from teammate Billy Wagner's suite - he retired his first 14 batters and beat Milwaukee 4-2 for his first major league win since 2003.
Notes: Hoffman (strained muscle on right side) is scheduled to make rehab appearances Tuesday and Friday for Triple-A Nashville. He is expected to come off the disabled list Sunday, when the Brewers are in Houston. ... Tatis made his first major league start and second appearance at second base, giving Luis Castillo a rest. ... Santos made his first start at catcher for the Mets, his fourth in the big leagues following three with Baltimore last year. He finished 2-for-4 with a double and a triple, his first extra-base hits in the majors. ... Mets CF Carlos Beltran and 3B Wright received their 2008 Gold Gloves before the game. ... Milwaukee's J.J. Hardy was called out on fan interference in the sixth, when a fan reached over the left-field railing and caught a foul fly that Murphy was under.
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