J.D. Davis and Brandon Nimmo also connected for the Mets, who were 4 1/2 games behind Milwaukee for the second NL wild-card berth going into the day.
New York starter Marcus Stroman walked the bases loaded with two outs and a 4-2 lead in the fifth.
Brad Brach (5-4) came on to get Eugenio Suarez to pop up on the first pitch. Suarez, second in the majors behind Mets rookie Pete Alonso with 48 home runs, slammed his black bat to the ground in frustration.
Alonso went 1 for 4 with a double to remain at 50 home runs. He was intentionally walked in the ninth, drawing a scattering of boos from Mets fans.
Alonso and Robinson Cano doubled in the first inning off Trevor Bauer. Wilson Ramos was hit by a pitch and Conforto launched a three-run homer, his 31st.
Eight of New York's nine hits went for extra bases.
The Reds scored in the first on Aristides Aquino's sacrifice fly, the first of 13 consecutive batters Stroman retired before Kyle Farmer hit his ninth homer, a two-out solo shot in the fifth.
Stroman allowed three hits and two runs with three walks and two strikeouts while lasting 4 2/3 innings, one out short of qualifying for the win.
Edwin Diaz pitched a scoreless seventh, Seth Lugo gave up Tucker Barnhart's 10thhomer leading off the eighth and Justin Wilson pitched the ninth for his fourth save after getting the loss on Saturday.
Bauer (11-13), in his 10th start since being acquired from Cleveland at the trade deadline, didn't walk anybody, but he hit two batters in seven innings. He gave up six hits and five runs with eight strikeouts.
Mets: Ramos was hit on the upper left arm with a pitch in the first inning. After being checked out by a trainer, the catcher stayed in the game. Bauer also hit Cano in the left foot with a pitch in the third. Cano left the game after the top of the fourth. X-rays on his big toe were negative.
Mets: LHP Steven Matz (10-9) starts at home Monday vs. Miami. He will try to bounce back from allowing seven runs on six hits in four innings in a 9-4 loss at Colorado last Monday.
Reds: RHP Sonny Gray (11-7) starts Tuesday at home vs. Milwaukee. His first strikeout will be his 200th of the season, extending his career high.
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Conforto mashes homer to right
Michael Conforto bashes a 3-run home run to right field in the top of the first inning.