Stauffer escaped a bases-loaded, no-out situation in the top of the 12th and Venable lined a game-winning single in the bottom of the inning off closer Craig Kimbrel to lift the Padres to a 3-2 victory over the Atlanta Braves on Saturday night.
Kimbrel (0-3) walked the bases loaded with one out before Venable hit a fastball on a line over the head of right fielder Jason Heyward, who was already playing shallower than normal.
''With that guy, the bases loaded and less than two outs and the winning run on third base, it takes the slider down out of play,'' Venable said. ''He doesn't want to end the game on a wild pitch. With him you have to get ready for the fastball anyway so it made things simple.''
Yangervis Solarte walked to start the 12th, and Jedd Gyorko and Chris Nelson drew consecutive one-out walks before Venable's game-winning single.
''When you go out there and throw a lot of balls and walk guys, that's what happens,' Kimbrel said.
Stauffer (3-2) pitched two innings but it was his escape in the 12th that kept San Diego in the game. The Braves loaded the bases with no outs, but Stauffer got Evan Gattis to hit into a third-to-home-to-first double play and retired Chris Johnson on a groundout.
''I think that was the game right there,'' Stauffer said. ''I think that kind of put the stamp on it.''
The Padres won for the fourth time in five games. Atlanta extended its losing streak to five games.
''All we needed was a lousy run and sometimes it's hard to get a lousy run,'' Braves manager Fredi Gonzalez said.
Atlanta tied the game at 2 in the eighth on Heyward's single, a walk and Johnson's RBI single.
Trailing 1-0, the Padres went ahead in the seventh. Rene Rivera led off with a single, was sacrificed to second and scored on Solarte's two-out single. After San Diego loaded the bases, Jordan Whalden relieved Ervin Santana and threw a wild pitch that allowed Solarte to score for a 2-1 lead.
Santana allowed two runs and six hits in 6 2-3 innings with six strikeouts and four walks.
San Diego's Tommy Medica had two more hits, including a second-inning single that gave him hits in six consecutive at-bats. Medica went 5 for 5 on Friday with two two-run homers, setting career highs for hits, RBIs and runs with four.
Braves: Heyward was back in the starting lineup after missing four games with a strained back. ''It's been four days, but it seems like it's been a month,'' Gonzalez said.
Padres: Right-hander Andrew Cashner (right shoulder soreness) will make a rehab start Friday with Single-A Lake Elsinore. ... Left fielder Carlos Quentin, on the 15-day DL (left knee soreness), will get a second opinion in Los Angeles sometime in the coming week. ... Catcher Yasmani Grandal (fluid in right knee) was out of the starting lineup for the third straight game.
Braves: Right-hander Aaron Harang (9-6, 3.43) pitches in the series finale at Petco Park where he resurrected his career by going 14-7 with a 3.64 ERA in 2011, his only season with San Diego.
Padres: Right-hander Tyson Ross (10-10, 2.60) has thrown eight consecutive games of six or more innings while allowing two or fewer runs, the longest streak in the NL and second in the majors to Seattle's Felix Hernandez, who has done it 14 straight games.
PASSING OF BRAVES BROADCAST LEGEND
Former Braves broadcaster Pete Van Wieren, 69, passed away Saturday morning after a long bout with cancer. ''One of the nicest people I ever met,'' Gonzalez said about Van Wieren, who broadcast Braves games for 33 years.
PRACTICE IS OVERRATED
Despite having little practice, the Padres ground crew did a commendable job in working the seldom-used tarp before the game at Petco Park, where a light drizzle hit in the afternoon. The Padres have had just 16 rainouts in 46 seasons, and only one in Petco's 10-year history
FINALLY OVER .500
The Padres went over the .500 mark at home (1,821-1,820) for the first time since Aug. 28, 2010.