Tied 1-1 in the eighth inning, pinch hitter Howie Kendrick lined a home run off ex-Nationals pitcher Craig Stammen over the left field wall. Shortstop Trea Turner followed Kendrick with a 425-foot home run to center field.
"I liked the first one, for sure," Nationals manager Dave Martinez said. "It put us ahead. Then it was wow, wow, and wow!"
Rendon, whose homer was his 12th of the season, called the feat "exciting."
"I think we were pretty fired up when Howie hit his because that gave us the lead," Rendon said. "It doesn't happen very often.
There have been nine times in MLB history where a team has hit four consecutive home runs. Former Dodgers and Red Sox outfielder J.D. Drew is the only player to be involved in two separate occurrences.
Drew hit the second of four straight home runs for the Dodgers in 2006. He was also the second player in line when the Red Sox homered four straight times against the rival Yankees a year later.
Drew and the Dodgers also accomplished the feat against the Padres.
Washington moved to 30-35 with the victory. The Nationals trail the first-place Philadelphia Phillies by seven games in the NL East Division.