Following this weekend's blockbuster trade that sent starters Samardzija and Hammel to the Oakland Athletics, Arrieta inherited the No. 1 role in the Cubs rotation.
The right-hander carried a perfect game into the seventh inning on June 24 against Cincinnati and went 7 2-3 innings without allowing a hit at Boston on June 30.
Washington ended such hopes immediately as leadoff hitter Span hit a fly ball that sailed over the outfielders for a double. Span moved to third base on Anthony Rendon's grounder to second and scored on Jayson Werth's groundout for a 1-0 lead.
But despite allowing runners in all but one inning, Arrieta escaped further trouble in the fifth, leaving runners on first and third after Rendon's inning-ending groundout. He then struck out Zimmerman and Bryce Harper to strand Werth on second in the sixth.
"He was never rattled," Renteria said. "He got ground balls when he needed to. He made pitches, threw them off balance a little bit. He did a nice job."
The Cubs threatened in the eighth, putting runners at second and third with one out against Tyler Clippard (6-2), but didn't score. Pinch-hitter Wellington Castillo struck out looking, and Ryan Sweeney grounded out.
Rafael Soriano pitched a perfect ninth for his 21st save for the Nationals, who have won seven of eight.
NOTES: The Cubs recalled RHP Blake Parker from Triple-A Iowa before the game. Parker takes the roster spot created by the trade with Oakland. ... Chicago hasn't announced who will replace Samardzija and Hammel when their rotation spots come up Wednesday and Thursday. Edwin Jackson (5-8, 4.99) will open the five-game series at Cincinnati on Monday against fellow RHP Mike Leake (6-7, 3.47).