Both Padres runners scored on a bizarre play as San Diego was down to its final out in the top of the ninth.
After Yonder Alonso led off with a single off Dodgers closer Kenley Jansen (4-3), Cabrera came in as a pinch runner and went to third on Venable's single.
One out later, Venable stole second, putting runners at second and third, but Mark Kotsay popped to second base for the second out.
Then, as Jensen had his backed turned to him while kicking dirt on the mound, Cabrera took off for home. A startled Jansen reacted by throwing high to catcher A.J. Ellis, who let the ball get away from him.
That allowed both Cabrera and Venable to score, handing the Padres the lead.
The unlikely comeback, nailed down by Huston Street's 1-2-3 bottom of the ninth, made a winner of Alex Hinshaw (1-1).
Andre Ethier went 3-for-5 with a two-run homer and four RBI for the Dodgers, who fell one-half game behind San Francisco in the National League West.