Bour hit his 14th home run for the Marlins, who got to 40 wins in 75 games — or 20 games faster than they did a year ago. Ichiro Suzuki's infield single in the fifth sparked what became a four-run inning that put Miami ahead for good.
The Cubs, with the best record in the majors, lost for the fifth time in six games. They ended a four-game skid Friday night despite giving up Bour's grand slam.
Clemens (1-0) trailed 4-1 early but settled down and gave Miami five innings of four-run ball. It was his first win since June 12, 2013, and A.J. Ramos got the last two outs for his 24th save in as many chances.
Addison Russell hit a three-run homer and Miguel Montero added a solo homer for the Cubs.