Goldschmidt's blast in the eighth inning off Carlos Marmol (2-4) broke a 4-4 tie and enabled the National League West-leading D-backs to break a two-game skid.
Kubel provided a bases-clearing double in the seventh and drove in another run to cap a four-run ninth.
Gerardo Parra went 2-for-3 with a solo homer and two RBI in the victory.
Willie Bloomquist added three hits and scored twice for Arizona, which banged out 17 in a game that was delayed nearly 2 1/2 hours by rain in the second inning.
Ian Kennedy (3-3) allowed four runs over seven innings to recorded the triumph, yielding three hits while walking one and striking out seven.
Nate Schierholtz went 2-for-4 with a solo homer and two RBI for the Cubs.