Dempster (4-3), making his first start since June 15 due to back muscle tightness, baffled the Mets on four hits and didn't issue a walk en route to the victory.
The 35-year-old right-hander struck out four while racking up his fourth win in four outings for the Cubs, lowering his National League-best ERA to 1.99.
Starlin Castro went 2-for-4 with a three-run homer and Geovany Soto's two-run single highlighted a big first inning that saw Chicago jump off to a 4-0 lead.
New York's Jonathon Niese (7-4) was lit up for seven runs on nine hits in a seven-inning start.
Swim Week Miami Beach 2014 [PHOTOS]