The Mets avoided a three-game sweep at the hands of the Reds, who had won five in a row.
Harvey (2-3), who made his major league debut less than three weeks ago, gave up four hits with eight strikeouts. In five starts he has struck out 34 batters.
The Mets built a 6-0 lead through six innings thanks in part to solo homers by Ike Davis and Jason Bay. Harvey helped his own cause with a two-run double during a three-run fourth inning.
New York's lead grew to 8-1 heading into the bottom of the ninth, but Cincinnati scored three times off reliever Frank Francisco.
The Reds had the tying run in the on deck circle when Jon Rauch came on to get the final out and record his third save.
Homer Bailey (10-8) suffered the loss after giving up six runs on eight hits in 5 2/3 innings.
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