Feldman (4-3) allowed seven hits, walked one and struck out six in the 109-pitch performance.
His two-bagger, scoring Nate Schierholtz and Welington Castillo, capped a four-run uprising in the fourth inning that broke a scoreless tie.
Anthony Rizzo went 2-for-4 with a solo homer and David DeJesus provided a two-run single for the Cubs, who evened the three-game series.
Mets starter Jeremy Hefner (0-5) yielded four runs on five hits in four innings.
Rick Ankiel went 2-for-4 with a two-run home run for New York.