Denard Span was the hero for the Nationals, pouncing on a throwing error from Jordan Pacheco to first to score the winning run from second base in the ninth inning in Washington.
Five of the Washington's past six wins have come in the form of walk-offs, while the National League East division-leading Nationals have won 10 games on the bounce.
The 10 successive wins is a franchise record for the Nationals.
"It's indescribable, really," said Span after the Nationals inflicted a six straight defeat on the Diamondbacks.
"I really don't have the correct or the right words to say what the feeling is other than saying that we just feel confident, that somehow, someway, we're going to find a way to inch off a victory."
The Nationals are seven games clear of the Atlanta Braves, who crushed the out-of-form Cincinnati Reds 8-0.
Julio Teheran allowed four hits through six innings as the Braves shutout the Reds and condemned the Cincinnati team to a six consecutive defeat.
In other results on Thursday, Brandon McCarthy pitched a four-hitter as the New York Yankees accounted for the Houston Astros 3-0.
McCarthy's eight strikeouts led the Yankees to a shutout win in New York.
The Los Angeles Dodgers were 2-1 winners over the San Diego Padres thanks to Justin Turner's two-run homer.
Clayton Kershaw also chipped in with 10 strikeouts and two walks as the National League West leaders stayed 3.5 games clear of the San Francisco Giants.
The Giants overcame the Chicago Cubs 5-3.
Fellow Los Angeles franchise - the Angels - downed the Boston Red Sox 2-0 for a fourth successive victory.
Kennys Vargas' homer inspired the Minnesota Twins to a 4-1 triumph against the Cleveland Indians.
Meanwhile, the Tampa Bay Rays edged the Detroit Tigers 1-0 to avoid a three-game sweep.