Both the Padres (50-60) and Braves (58-53) had plenty of opportunities to end this one earlier after mounting comebacks late in the game, but neither could break through until Venable smashed a fastball from Kimbrel over a leaping Jason Heyward to bring home Yangervis Solarte.
"Both teams kept pitching, both teams threatened, both teams made some plays," said Padres manager Bud Black. "There was a little bit of everything in there."
Solarte had the Padres' only other hit with runners in scoring position in 13 at-bats. His two-out RBI single off Ervin Santana in the seventh tied the game at one before a wild pitch from Jordan Walden later in the inning gifted San Diego a 2-1 lead.
But Kevin Quackenbush immediately coughed it up in the eighth. Chris Johnson hit an RBI single with one out to score Heyward, advance Evan Gattis to third and even the score at 2, with the Braves looking poised to retake the lead.
After that, though, Atlanta was 0-for-10 with runners in scoring position, as they were handed a second straight demoralizing loss after being drubbed 10-1 in Friday's series opener. The Braves have lost five in a row overall to fall to 2 1/2 games back in the NL East.
"We had a lot of opportunities with the right people hitting," said Braves manager Fredi Gonzalez. "All we needed was one lousy run. It's hard to get a lousy run sometimes. But we had plenty of opportunities to do it."
The Padres managed to keep Atlanta from capitalizing on prime chances to score in each extra inning, none bigger than the 12th.
The Braves loaded the bases with no outs, but after a mound visit from Black, Tim Stauffer (3-2) coaxed a 5-2-3 double play from Gattis.
"It's not where you're trying to be," Stauffer said of having the bases loaded with no outs. "[Black] said, 'Let's go with the best pitch here and get a ground ball.' So that's what we did. It was a curveball, down and away. Fortunately, [Gattis] hit it and we got the ground ball."
Then, Chris Nelson -- playing his first inning in the Majors as a first baseman -- made a diving stop to retire Johnson, deflate the Braves and set the stage for the Padres' comeback in the bottom half.
"That's a game-saver," Black said of Nelson's play.
An uncharacteristically wild Kimbrel then walked Solarte, Jedd Gyorko and Nelson -- all on full counts -- before Venable's game-winner with one out.
"We had really good at-bats that gave us a chance," said Venable, who's hitting .327 since the All-Star break. "That's how you beat a guy like that -- make him work a little bit."
Santana had hurled eight scoreless innings against the Padres in Atlanta on Monday, and he once again stymied the Friars for most of his outing Saturday.
The right-hander allowed just three hits through his first six frames before the Padres finally got to him in the seventh to set off the wild chain of comebacks. Santana exited after 6 2/3 innings and was charged with two earned runs on six hits with four walks and six strikeouts.
Ian Kennedy, who missed his last start with a minor oblique injury, battled control issues (five walks) that shortened his outing. He lasted just five innings but threw 101 pitches.
At the same time, he only allowed two hits and one run with seven strikeouts, so he was mostly satisfied with the results -- even more so with what happened long after he exited.
"Five walks was a lot, but looking back on it, you just go out and get through it -- and it was a fun game to watch," Kennedy said. "It's always fun when you win those type of games."