Chatwood (6-3) turned in his third consecutive start of allowing two or fewer runs. The Cubs reached the right-hander for seven hits and four walks but turned them into just two runs. Chatwood struck out two Chicago batters.
Josh Outman, Edgmer Escalona and Matt Belisle teamed up for two innings of shutout relief and Rex Brothers gave up an unearned run in the ninth before notching his fifth save as the Rockies took two-of three from Chicago.
Gonzalez easily scored the go-ahead run and Cuddyer followed him home on an errant throw from center fielder Junior Lake, giving the Rockies what turned out to be the decisive run.
Jackson (6-11) was hung with the loss, coughing up four runs (three earned) on five hits over seven innings.
Starlin Castro went 4-for-5 with a run scored and Anthony Rizzo homered for the Cubs.