The loss marked the 29th time this season the Phillies have lost by one run.
Rosario's blast came on a Hector Neris 2-1 fastball, a pitch right down the middle of the plate.
The Phillies manufactured three runs in the opening frame with Nick Williams and Tommy Joseph each collecting RBI singles. The Mets answered with the long ball, scoring four runs over the next two innings via homers by Yoenis Cespedes and Michael Conforto.
Trailing 6-5 in the eighth, Cesar Hernandez's worked a seven pitch at-bat before launching a solo shot off Mets' reliever Jerry Blevins to even the contest.
Neris surrendered three hits in the ninth, including Rosario's homer.
Rhys Hoskins, hitting in the cleanup spot for the Phillies in just his second big league game, finished 0-for-4 on the night with a walk and scored a run. He came to the plate four times on the night with runners in scoring position and left five runners on base.
Phillies' starter Nick Pivetta tossed just 4 2/3 innings, surrendering six runs on seven hits.
The two clubs resume their four-game set on Saturday with righty Aaron Nola scheduled to face left-hander Steven Matz.
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