Span scored from second on third baseman Jordan Pacheco's throwing error in the ninth inning, and the Nationals stretched their winning streak to 10 games with a 1-0 victory over the Arizona Diamondbacks on Thursday.
"We just feel confident that somehow, some way we're going to find a way to inch off a victory," Span said.
Five of Washington's last six wins have come in its final at-bat of the game, and the win streak is tied for the franchise record. Kansas City is the only other team to win 10 consecutive games this year.
"It's not how you plan it," Nationals manager Matt Williams said.
Rafael Soriano (4-1) pitched a scoreless ninth for the Nationals, who swept three-game series against the New York Mets and Pittsburgh Pirates before winning all four games of this series.
Washington's ninth hit was a one-out single for Span against Oliver Perez (2-3). Evan Marshall then came in and Span swiped second. But Anthony Rendon followed with a chopper to third.
Pacheco's throw bounced off the dirt and into the first-base camera well, and Span was awarded home.
"That what's guys like me, speed guys, dream of," said Span, who set a career high with his 27th stolen base. "That's way more important than stealing two or three bags in the first five innings."
The Diamondbacks have lost six straight for the second time this season and dropped to 5-14 in August. Eight of Arizona's last 10 games have been decided by one run.
"I guess some losses are a little more difficult," first baseman Mark Trumbo said. "I think we battled as well as we could. Just didn't have too much offense to show for it."
The Nationals also struggled at the plate, going went 0 for 13 with runners in scoring position.
Gio Gonzalez pitched seven innings for Washington in his longest outing since July 26, and his first without an earned run since July 5. He allowed four hits and walked three while lowering his career ERA against Arizona to 1.33 in three starts.
"I just wanted to try and blend in with the rest of the rotation," said Gonzalez, who is 0-5 in his last eight starts. "You try not to stick out like a sore thumb."
Somehow, Wade Miley matched Gonzalez for 6 2-3 innings despite allowing eight hits and walking a season-high six batters.
Miley retired Adam LaRoche three times to end an inning -- twice on double plays -- before walking him to load the bases with two out in the seventh. Matt Stites got Wilson Ramos to fly out to right to end the threat.
Nationals: INF/OF Ryan Zimmerman (right hamstring strain) threw on the field for the first time since going on the disabled list July 23. There is no specific timetable for his return. "You have to use that muscle to throw," Williams said. "It's part of the strengthening process." ... INF/OF Steve Souza (right shoulder strain) joined Single-A Hagerstown to begin a rehab assignment. ... OF Nate McLouth was scheduled to have season-ending shoulder surgery Thursday, Williams said.
Diamondbacks: INF Chris Owings (left shoulder strain) will continue his rehab assignment at Triple-A Reno on Friday after going 4 for 7 in three games with Arizona's rookie league club. . OF A.J. Pollock (fractured right hand) took light batting practice Thursday.
Nationals: RHP Doug Fister (12-3, 2.20 ERA) looks for his third win in August in the first of a three-game set at home against San Francisco.
Diamondbacks: RHP Josh Collmenter (8-7, 4.31 ERA) will make his fifth career start against San Diego on Friday as Arizona begins an eight-game, 10-day homestand.
With two outs in the fifth, left fielder Bryce Harper made life more difficult for Gonzalez by over-running Miley's single, allowing Alfredo Marte to reach third, and then throwing to home as Miley took second.
Gonzalez walked Ender Inciarte to load the basis, but escaped on Cliff Pennington's popout to first.
Trumbo became just the second Diamondbacks runner in 12 attempts to be caught stealing when Wilson Ramos threw him out at second to end the sixth.
Nationals Walk Off Against Diamondbacks
Baseball Tonight Spotlight: Denard Span scored on a throwing error in the bottom of the ninth to lift the Nationals past the Diamondbacks 1-0, stretching Washington's winning streak to 10 games.