Niese (5-3) pitched a season-high eight innings and gave up three hits, one a homer to Carlos Ruiz. His hit in the second inning put New York up for good.
The Mets put on a clinic of clutch hitting and slick fielding in handing the Phillies their sixth straight loss. The only thing they did wrong was run into two outs on the basepaths.
Daniel Murphy finished a homer short of the cycle, doubled twice, drove in four runs and made a leaping catch and diving stop at second base.
Ruben Tejada had an RBI single among his three hits. He also put on a show at shortstop for the boisterous crowd of 42,516, the highest attendance in the four-year history of Citi Field.
Tejada led off the game with an 11-pitch out and it rarely got much easier for Vance Worley (4-5) and Philadelphia's bullpen. New York increased its NL-best run total with two outs to 178 and had 15 hits overall.
Wright, tied for second behind Ruiz in the NL batting title race, drove in four runs with an RBI grounder in the first and the long ball to straightaway center field in the sixth that made it 9-1.
Ruiz homered on Niese's first pitch of the second inning into the party deck in left field. But it was no party for the falling Phillies. They dropped to a season-worst 10 games under .500 at 36-46.
It's been quite a reversal of fortunes for the two rivals. Finally almost at full health for the first time in several seasons, the Mets have pitched their way to second place in the NL East. The five-time division champion Phillies, meanwhile, have been beset by injuries and a stunning subpar performance from its staff - other than All-Star Cole Hamels. And he's been the subject of recent trade speculation.
Philadelphia manager Charlie Manuel said before the game that the three weeks leading up to the non-waiver trade deadline on July 31 are crucial for the Phillies, who have been in a tailspin since ace Roy Halladay went out with an injury to the right upper back. They were 25-24 after Halladay's last start on May 27 but entered Tuesday with the club's worst record at the midpoint of the season since 1997.
They got off to a horrid start Tuesday.
The Mets jumped on Worley in the second and could've had a big inning if it weren't for a couple of good throws that nailed aggressive baserunnsers.
With the bases loaded, Niese singled in two runs to match his career high for RBIs in a game. But Josh Thole was thrown out by center fielder Shane Victorino trying to advance from first to third on the play.
Murphy followed Tejada's single with an RBI double, the Mets fifth straight hit. A perfect relay from left fielder John Mayberry to shortstop Jimmy Rollins to Ruiz cut down Tejada at homeplate, ending the inning.
Worley had not given up more than three runs since giving up five May 5 - six starts - but topped his season high in just four innings this time. He allowed 10 hits and six runs in dropping the starters' record to 11-22 over the last 43 games.
NOTES: Phillies 1B Ryan Howard (Achillies) was scheduled to play his sixth rehabilitation game. He went 1 for 4 with RBI and a double Monday for Triple-A Lehigh Valley. ... Wright has hit at least 10 homers in a season nine times, breaking the Mets record held by Mike Piazza, Darryl Strawberry and Ed Kranepool.