Alex Hinshaw (1-1) recorded two outs to get the victory, ending the Padres' 10-game losing streak at Dodger Stadium. All-Star Huston Street worked a perfect ninth for his 14th save in 14 attempts.
Jansen (4-3) ended up with his fourth blown save opportunity in 20 chances.
Yonder Alonso and Venable sparked the winning rally with consecutive singles, putting runners on the corners with none out. Jansen then struck out Cameron Maybin at the end of a grueling 11-pitch at-bat and retired pinch-hitter Mark Kotsay on a popup after Venable stole second.
Alexi Amarista worked the count to 2-2, and Cabrera saw an opening while Jansen kicked the dirt in front of the rubber a couple of times with his back turned away from third. He dashed for home and a stunned Jansen threw the ball all the way to the screen, allowing the go-ahead run to score.
Andre Ethier had four RBIs for the Dodgers in his second game off the disabled list, belting a tiebreaking two-run homer and a pair of RBI singles. Aaron Harang allowed four runs, three earned, and four hits over seven innings against his former team.
The Padres tied it at 4 in the sixth when Chase Headley followed a leadoff walk to Logan Forsythe with his ninth home run into the right-field pavilion on an 0-2 pitch.
But the NL West leaders responded in the bottom half against rookie reliever Brad Brach. Matt Kemp reached on a two-out infield single for his fifth hit in eight at-bats since coming off the DL, and Ethier sent his 11th homer to right-center.
Ronald Belisario relieved Harang and yielded a two-out RBI single to Carlos Quentin in the eighth.
Padres starter Edinson Volquez threw 111 pitches over five innings, giving up four runs, eight hits and four walks while striking out six. The right-hander has walked three or more batters in each of his last 11 starts - one short of the Padres' club record in one season, set by Dave Freisleben in 1974.
Ethier, who leads the Dodgers with 59 RBIs, tied it at 1 in the first with a bloop RBI single that fell in short left field between Quentin and shortstop Amarista after some miscommunication between the two.
Ethier singled home Bobby Abreu with the bases loaded in the third before Volquez forced in another run with a walk to Juan Rivera. The right-hander, who leads the majors with 67 walks, minimized the damage by retiring his next three batters.
Quentin hit a leadoff homer to center field in the fourth, his eighth this season, but the Dodgers got that run back in the fifth on Adam Kennedy's RBI double.
Kennedy started at third base in place of Juan Uribe, who is mired in a 1-for-33 slump and has only five home runs in 401 at-bats with the Dodgers - after hitting a career-high 24 in 2010 with San Francisco.
NOTES: This was the first time this season that Headley and Quentin, the Padres' 3-4 hitters, homered in the same game. ... Volquez came in with the worst run support in the majors when he is in the game (2.52). This was the eighth time in his 19 starts that the Padres scored more than two runs, but his record in those games is 3-3 with two no-decisions. ... Dodgers RHP Javy Guerra was placed on the bereavement list and returned to his native Mexico, where his father had a heart attack Friday night. RHP Josh Wall, who has yet to appear in a big league game, was promoted from Triple-A Albuquerque to fill the roster spot.