Juan Francisco slapped a one-out triple in the right-center field gap off of Dale Thayer (0-3) to set-up Stubbs for the squeeze that went toward third base.
Francisco Cordero earned his 37th save although he walked four in the 13th. Justin Turner hit into a game-ending unassisted double play when he lined out to Todd Frazier at second.
Jay Bruce had three hits, including a two-run homer for the Reds, who have won three straight.
Sam LeCure (2-1) picked up the win with a 1-2-3 12th.
Jose Reyes (.336) continued his pursuit of the first NL batting title in Mets history by going 3-for-6 with a pair of solo home runs. He leads the Brewers' Ryan Braun (.335) ,who went 1-for-2 in Tuesday's game against the Pirates.
Bruce gave the Reds a quick 2-0 lead in the first inning with a line-drive home run down the right-field line. The Mets gave Cincinnati another opportunity when they were unable to turn a double play when Joey Votto grounded to second, as Reyes bounced his throw to first.
The Mets cut Cincinnati's advantage in its half in the home first with an RBI single by David Wright.
Reyes tied the game in the third with a solo shot to right-center field, and then gave the Mets a 3-2 lead in the fifth when he circled the bases a second time in as many at-bats.
Votto belted an opposite field home run to left-center field to even the score again in the sixth.
Nick Evans laced a one-out double in the home sixth, and Josh Thole brought him home with a single up the middle to make it a 4-3 game.
Francisco tied it up in the ninth with a two-out double, which plated Dave Sappelt who came on to pinch run for Devin Mesoraco. Mesoraco slapped a single to left, and reached second when Edgar Renteria singled.