Nelson Figueroa (3-3) pitched a scoreless seventh to earn the victory in relief of Johan Santana. Luis Ayala pitched the ninth for his fourth save in five chances.
Gagne (4-3) gave up three runs and four hits in the eighth. He has a 6.81 ERA this year after signing a $10 million, one-year contract with the Brewers.
Six Milwaukee relievers allowed four runs and seven hits with four walks in the final four innings.
Trailing 2-1, Daniel Murphy greeted Gagne with a double. One out later, Delgado hit his 31st home run of the year to give New York a 3-2 lead.
It was Delgado's 462nd career homer, tying him with Jose Canseco for 31st place on the all-time list. The Mets first baseman has 20 homers and 60 RBI since June 27, the most of any NL player in that time.
Carlos Beltran singled and scored on Ryan Church's double to the center-field wall, increasing the Mets' lead to 4-2. Beltran later left the game with a right knee contusion, but the severity of that injury was not immediately known.
New York starter Johan Santana pitched six innings, giving up two runs and seven hits. He struck out 10.
Sheets had given up only two hits and a walk before being pulled. The right-hander - counted on along with CC Sabathia to lead the Brewers back to the playoffs for the first time since 1982 - put on a team jacket and stayed in the dugout talking with manager Ned Yost and pitching coach Mike Maddux after leaving the game.
A year after blowing a seven game lead in the final 19 days of the season, the Mets fell behind quickly in their first game of September. Milwaukee made it 1-0 in the first when J.J. Hardy's liner to left hit off Murphy's glove and rolled into the left-field corner. Murphy slipped on the warning track and Hardy slid into third with a triple.
Ryan Braun followed with a double to left to make it 1-0.
Santana balked with Prince Fielder on third in the sixth, giving the Brewers a 2-0 lead.
The Mets scored their first run in the seventh on reliever Mitch Stetter's wild pitch, allowing Beltran to score from third. Stetter then got Jose Reyes to fly out with runners on second and third to preserve the lead.
