Last season's NL Rookie of the Year, deGrom was joined by Rafael Montero, Jeurys Familia, Jenrry Mejia and Jerry Blevins in completing a three-hitter.
Wright went 3 for 3 with a walk, and Juan Lagares had three hits.
Mets pitchers extended their scoreless streak to 20 1-3 innings and have given up only nine runs over the past seven games.
The Rangers have lost eight in a row.
Wright doubled home Lagares in the first inning against starter Logan Verrett, a former Mets minor leaguer who was making his Rangers debut after being acquired Thursday on a waiver claim from Baltimore.