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The Mets trailed 5-1 and 8-3 before they went on a four home-run spree, capped by Juan Lagares' three-run shot in the sixth to give the Mets the 10-8 lead.
It was the biggest comeback for the Mets this season, topping their rally from a three-run deficit to beat Miami.
Darrell Ceciliani hit his first major league homer in the fourth, when Dilson Herrera followed with another solo shot one out later.
Travis d'Arnaud brought the Mets within 8-7 with a two-run homer in the fifth off Braves reliever Brandon Cuniff after he replaced starter Mike Foltynewicz (4 1/3 innings, six runs (five earned), nine hits).
Curtis Granderson was 3-for-5 and scored twice, as did Lucas Duda and d'Arnaud. . .Lagares also was 3-for-5.
The Mets bullpen was solid, capped by Jeurys Familia's four-out save. Sean Gilmartin pitched two hitless innings, Bobby Parnell one (after a leadoff walk) and Hansel Robles, Saturday's goat, got the first two outs of the eighth before Familia entered and earned his 19th save.
Familia got out of the eighth thanks to a diving stop-and-glove shovel from Herrera, who got the ball to Wilmer Flores in time to get Cameron Maybin.
Gee escaped with a no-decision after giving up eight runs and 11 hits in 3 2/3 innings. Jace Peterson hit a three-run homer in the second off Gee, who was making a spot start in his return from the bereavement list after his grandfather died.
Nick Markakis knocked out Gee with an RBI double with two out in the fourth, and Kelly Johnson's RBI single off Alex Torres scored the third run of the inning.
The Mets begin the first half of a four-game home-and-home series against the streaking Blue Jays at Citi Field Monday (7:10 p.m., SNY). Noah Syndergaard (2-4, 4.15), who Toronto traded to the Mets along with d'Arnaud for R.A. Dickey in 2012, faces Mark Bueherle (7-4, 4.25). Toronto has won 11 in a row.