Jackson singled home Chris Young with one out in the tenth inning to lift Arizona to a 4-3 victory over the Atlanta Braves, the Diamondbacks' eighth straight win.
"It doesn't matter what the score is," Jackson said. "It doesn't matter what the inning is. We never feel we're out of the game."
Jackson was 3-for-5 with two RBIs and Young hit his third homer in four games for the Diamondbacks, who won in their final at-bat for the third straight game. Eric Byrnes and Tony Clark homered to end each of Arizona's last two contests.
Arizona has seven game-winning hits this season.
"I don't even know if I can put it into words," Young said. "It's been exciting."
Tyler Yates, the Braves' fourth pitcher, walked Young on four pitches to lead off the tenth. Orlando Hudson sacrificed Young to second and Byrnes was intentionally walked.
Yates (2-3) gave way to Chad Paronto, and Jackson looped Paronto's first pitch into shallow left field.
"I know he has a good sinker," Jackson said. "I was looking for something early in the count, because when you get two strikes against a guy with a good sinker you're probably going to hit a ground ball."
Juan Cruz (5-1) struck out two of the three batters he faced in the 10th for the win.
"It's the bullpen and it's been the whole bullpen," said Arizona manager Bob Melvin. "In extra-inning games everyone has to contribute."
Atlanta lost its fourth straight. "I did the cardinal sin of walking the leadoff batter in extra innings," Yates said. "As soon as that happens it's almost guaranteed to be a man on second with one out."
The Braves' best chance to win came in the eighth. Atlanta had runners on first and second with one out against reliever Tony Pena, but Jeff Francoeur grounded into an inning-ending double play.
"Frenchy hit the ball hard right at the third baseman," Cox said. "First and second and a double play, but he scorched it."
For the second straight game, the Diamondbacks squandered an early lead.
Young's fourth leadoff home run of the season off John Smoltz gave the Diamondbacks a 1-0 lead. Arizona added two more in the third on singles by Young and Hudson, Byrnes' sacrifice fly and an RBI double from Jackson.
Atlanta tied the game in the fourth. Chipper Jones drew a leadoff walk, Francoeur also walked and Matt Diaz brought both home with a double to left to make it 3-2. Brian McCann grounded out and Julio Franco was intentionally walked before Smoltz singled off Mark Reynolds' glove at third, scoring Diaz to tie game at 3.
Starter Doug Davis settled in after Smoltz's single and retired nine of the final 10 batters he faced. Davis allowed the three runs and five hits over seven innings with three walks -- one intentional -- and six strikeouts.
Smoltz was just as solid, allowing the three runs and seven hits over seven innings with six strikeouts and no walks.
"We're not winning the close ones, not to overstate the obvious," Smoltz said. "When a team's hot like Arizona, it seems like they're almost winning every game they have to win, whether it's in the last at-bat or by making plays."
Arizona is the first team with three straight game-winning hits since the Milwaukee Brewers on May 13-17, 2006. The Diamondbacks previously had three straight game-winners from May 10-12, 1999. ... The Diamondbacks led 7-0 on Friday before pulling out an 8-7, 11-inning victory over the Braves. ... Young also led off Arizona's 7-0 win over Florida with a home run. ... It was the second time this season Smoltz had not walked a batter. ... Byrnes' sacrifice fly was the Diamondbacks' major-league leading 45th of the season. ... Davis leads the NL with 72 walks in 131 1-3 innings pitched.