Leake (7-1) stretched his unbeaten streak to five straight starts by holding the Nationals to five hits and a walk while fanning three before the rains came at Great American Ball Park.
Leake also notched an RBI for the Reds, who have won four of five games coming out of the All-Star break.
Nationals starter Luis Atilano (6-7) was limited to just four innings because of the weather and gave up five runs on five hits with three walks.
Mike Morse hit a three-run, pinch-hit triple and Ryan Zimmerman hit a two-run homer during a six-run sixth inning for Washington, which has lost four straight and six of seven overall. Nyjer Morgan had two hits and drove in one run in the loss.
Morgan knocked in Adam Kennedy with a two-out base hit in the third, but Cincinnati came back with two runs in the fourth as Leake poked an RBI single to center and Cabrera scored another with a groundout.
Doug Slaten took the mound to begin the bottom of the fifth following the lengthy delay, walked Votto and gave up a single to Jonny Gomes that left runners at the corners. Jay Bruce made it a 6-1 game with a groundout.
Miguel Cairo reached on a base hit and stole second with two outs to put two in scoring position. Zimmerman made a diving stop up the third-base line on a hot smash by Corky Miller but the throw skipped by Adam Dunnat first. It was ruled a single and both runs scored, one unearned, for an 8-1 Reds lead.
Cincinnati went with Micah Owings on the mound to start the sixth and the Nationals scored six times in the inning to make it a one-run game.
Owings promptly walked Dunn to start things off and Zimmerman drilled a two- run homer down the right-field line for an 8-3 game. Josh Willingham was drilled with a pitch, but Owings seemed to be working out of trouble after getting consecutive outs. He then walked Kennedy and gave way to Bill Bray, who walked Willie Harris to load the bases.
Morse stepped to the plate and lined a triple off the base of the right-field wall, clearing the bags for a sudden 8-6 score. Ian Desmond doubled to left to score Morse for a one-run difference.
Tyler Clippard restored a measure of order with a 1-2-3 bottom half for Washington. Nick Masset and Arthur Rhodes combined to hold the visitors scoreless in the seventh and eighth before Francisco Cordero pitched a perfect ninth for his 26th save.
Leake has allowed two or less earned runs in 10 of his 18 starts this season...Miller had two hits for the Reds...The rain delay lasted 2 hours, 40 minutes...Both teams left five men on base.