Santana (2-2) allowed three runs and four hits, outpitching Cole Hamels in a matchup of two of the best left-handers in the majors.
Wright finished 4-for-4 with two RBIs and a walk.
Pinch-hitter Greg Dobbs hit a three-run homer off reliever Aaron Heilman to cut the Phillies' deficit to 5-4 in the eighth, but the Mets bullpen held on. Billy Wagner pitched a perfect ninth for his third save.
Facing the defending NL East champions for the first time since joining New York, Santana showed why the Mets made him the highest-paid pitcher in major league history.
The two-time AL Cy Young award winner kept a potent lineup off balance with his trademark changeup while mixing in quite a few sliders.
Hamels (2-2) gave up five runs - four earned - and eight hits in seven-plus innings.
The Mets beat the Phillies for the third straight time after losing nine in a row over two seasons. Jimmy Rollins, the 2007 NL MVP, has been out of the lineup for each of New York's wins. He hasn't started the last nine games since spraining his left ankle in a win over the Mets on April 8.
When New York acquired Santana from Minnesota in late January, the move prompted Carlos Beltran to declare the Mets were the team to beat in the division. That was a right-back-at-you message to Rollins, who made the bold prediction last year and followed through by leading the Phillies to their first NL East title in 14 years.
Santana certainly delivered in his first start against the Phillies in six years. He left after allowing consecutive singles to start the bottom of the eighth. Heilman entered to face Dobbs, who drove a pitch into the right-field seats.
Carlos Delgado's sacrifice fly off Brad Lidge gave the Mets a two-run cushion in the ninth. First baseman Ryan Howard's error
- the 17th committed by the Phillies this season - led to the unearned run.
After Chase Utley's homer to center cut it to 2-1 in the seventh, the Mets added insurance runs.
Ryan Church led off the eighth with a single and Wright followed with a double. J.C. Romero replaced Hamels after an intentional walk to Beltran loaded the bases, and Delgado drove in a run with an groundout. Angel Pagan's RBI double and Brian Schneider's run-scoring single made it 5-1.