Wright went 4 for 5 with two of New York's season-high seven doubles to help the Mets take two of three in Philadelphia after winning a five-game series at first-place Atlanta.
With the team making a major marketing push to get Wright elected to start next month's All-Star game at Citi Field, the third baseman is batting .405 with 14 extra-base hits in his last 17 games.
Given a rare heaping of run support, Harvey (7-1) allowed two hits in six innings and struck out six to earn consecutive wins for the first time since mid-April.
The 24-year-old right-hander tossed four perfect innings and threw a season-low 72 pitches - his outing was cut short by a 20-minute rain delay in the seventh.
Harvey also hit an RBI double to deep right-center and scored in a three-run fifth that made it 4-0. Later, he hit a line drive that knocked reliever Joe Savery's glove off his hand but was thrown out at first.
Harvey became the first Mets starter to win twice in one season at Citizens Bank Park.
Wright hit his 12th home run in the ninth and finished a single shy of the cycle. The club said the previous Mets player to have four extra-base hits in a game was Edgardo Alfonzo on Aug. 30, 1999, at Houston.
New leadoff batter Eric Young Jr. had three hits and scored twice.
Philadelphia's only threat against Harvey came in the fourth, when Chase Utley hit a leadoff double and Ryan Howard worked a one-out walk. But Harvey got out of the jam by striking out Domonic Brown on a 99 mph fastball and retiring Delmon Young on a grounder.
New York opened the scoring in the first when Marlon Byrd drove in Young with a sacrifice fly.
In the fifth, Harvey helped himself by hitting the first of three RBI doubles for the Mets. Juan Lagares led off the inning with what appeared to be an easy fly to center, but Ben Revere fumbled the ball in the exchange from his glove to his bare hand and it was ruled it a three-base error, opening the door for New York.
The Mets added two more in the sixth. Josh Satin and John Buck drew back-to-back walks before Lagares chased Phillies starter John Lannan (0-2) with an RBI double. Buck scored on Omar Quintanilla's sacrifice fly to make it 6-0.
Byrd hit an RBI double in the seventh after Wright's triple.
Mets relievers LaTroy Hawkins and Brandon Lyon closed it out, handing the Phillies their seventh shutout of the season.