The Phillies were within one strike of claiming a victory, but the Mets got to Jonathan Papelbon to claim their sixth win in eight games.
With Philadelphia holding a one-run lead heading into the bottom of the ninth, Papelbon (2-3) gave up a leadoff double to Ike Davis. Ronny Cedeno ran for Davis and went to third on a sacrifice by Josh Thole, after which Kirk Nieuwenhuis struck out.
Papelbon then hit pinch-hitter Jordany Valdespin with a pitch and walked Ruben Tejada on a 3-2 offering to load the bases. Daniel Murphy drove in the tying run with an infield single and Wright hit the first pitch from Papelbon to right for the game-winning hit.
Wright had four RBI in the contest, also producing a run in the third with a single and then delivering a two-run homer in the fifth.
Bobby Parnell (2-1) got the win by striking out two during a perfect top of the ninth.