Penny (5-3) allowed 10 runs in 4 2-3 innings, the most off him in 236 career big league starts. He gave up 10 hits for the third time in eight starts this season.
Luis Castillo, David Wright and Raul Casanova also drove in two runs apiece, helping the Mets avoid getting swept in the three-game series.
Penny fell behind 4-0 in the second when former-Dodger Marlon Anderson hit an RBI single, Casanova followed with a two-run single and Castillo added a two-out RBI single.
Carlos Beltran led off the third with a single and scored New York's fifth run on Angel Pagan's groundout. The Mets blew it open with a six-run fifth that equaled a season high for runs in an inning.
Maine singled with the bases loaded to make it 7-0, and Penny departed after walking Jose Reyes. Former New York Yankee Scott Proctor walked Castillo, forcing in a run, and David Wright - in a 1-for-20 funk - hit a two-run double. Castillo scored on Proctor's wild pitch.
Church led off the sixth against Proctor with his sixth homer and second in two days.
Pagan, starting in left field while 41-year-old Moises Alou got the day off, turned in the defensive play of the game in the first when he somersaulted into the first row of the box seats and held onto Andre Ethier's foul fly.
Pagan remained on the hard cement for a few anxious moments but returned to his position, rubbing his left shoulder and flashing a huge grin as the partisan Dodger crowd of 40,696 applauded his effort. He left in the third with tightness in the shoulder after sliding headfirst into second.