Kennedy (10-3) reached double figures in wins for the first time, taming the Dodgers on five hits and three wallks, allowing two runs. He fanned seven.
Joe Paterson and Sam Demel combined for a scoreless eighth and David Hernandez earned his eighth save with a 1-2-3 ninth for the Diamondbacks, who evened their three-game set with Los Angeles.
The D-backs got all their scoring in the second when Allen erased a 1-0 Dodgers lead with a three-run blast, scoring Miguel Montero and Geoff Blum ahead of him.
Hiroki Kuroda (6-11) was saddled with the loss, yielding three runs on five hits in a six-inning start for Los Angeles.
Matt Kemp knocked a solo homer for the Dodgers.