Bud Norris (6-8) allowed three runs and six hits in his first win since July 6. The right-hander was 0-1 with a 3.91 ERA in his previous four starts.
Aramis Ramirez hit a two-run homer and Geovany Soto had a solo shot for the Cubs, who had won four straight series. Ramirez, Soto and Darwin Barney each had two hits.
Chicago had several chances but struggled with runners in scoring position all day long.
The Cubs' last opportunity came in the ninth, when Barney hit a leadoff single against Melancon and moved to third on Ramirez's perfectly placed grounder up the middle.
Melancon retired Carlos Pena on a popup before pinch-runner Tony Campana swiped second to put runners on second and third with one out. Soto then tapped to shortstop Clint Barmes, who threw to third to catch Barney in a rundown. Marlon Byrd grounded out to end the game, giving Melancon his 12th save.
Coleman (2-5) allowed four runs and a career-high 10 hits in 3 2/3 innings while filling in for Zambrano, who was placed on the disqualified list Saturday following a meltdown in Atlanta last week when he talked about retirement and left the team.