Delgado's double off Dempster (2-4) followed a leadoff walk to David Wright as the Mets (62-47) moved 15 games over .500 for the first time since early June. Delgado scored on Shawn Green's two-out double inside the third-base line for a 4-2 lead.
Green came in on an RBI single by Ruben Gotay, pinch-hitter Moises Alou singled and Jose Reyes got the Mets' fifth hit of the inning, another run-scoring single that led to boos among the 41,512 fans at Wrigley Field.
Guillermo Mota (1-0) pitched out of an eighth-inning jam to gain his first major league win since serving a 50-game suspension for a positive steroid test.
Chicago ace Carlos Zambrano, bidding for his major league-leading 15th win, left in the sixth inning because of heat-related cramping. Zambrano gave up two hits, including a homer to Ramon Castro, and tied a career high by walking seven in five-plus innings.
Mets starter Orlando Hernandez allowed two runs and five hits, including a sixth-inning homer by Derrek Lee. Jason Kendall hit a two-out RBI double off the ivy-covered wall in left to tie the game at 2-2 in the seventh, finishing El Duque, who struck out nine and walked one.
Marlon Anderson's two-out RBI single in the seventh put the Mets ahead 2-1 after reliever Carlos Marmol walked two batters.
Lee reached third in the bottom of the inning after a single, stolen base and throwing error on Castro before Aramis Ramirez flied out against Mota.