They're on the brink of duplicating that feat, but will need to overcome a key absence in order to sweep this three-game set against the last-place Rockies on Wednesday.
The Nationals (55-43) won five in a row from June 28-July 2, completing the stretch with three straight home victories over Colorado (40-60).
Washington, which leads second-place Atlanta by two games in the NL East, has a chance to match it after beating the Rockies for the ninth time in 11 meetings with a 7-4 victory Tuesday.
The Nationals, though, will be without Ryan Zimmerman, who left in the sixth inning with a strained right hamstring. The third baseman, who missed 44 games with a broken right thumb earlier this season, was placed on the 15-day disabled list after getting hurt while running out a grounder.
Zimmerman has gone 12 for 33 (.364) with 11 RBIs in the last nine games. Manager Matt Williams says Zimmerman had an MRI on Wednesday and remains ''pretty sore,'' and the team recalled infielder Zach Walters from Triple-A Syracuse.
Ian Desmond could pick up the slack by continuing a hot stretch during which he's batting .400 with 13 RBIs in 14 games, which includes three versus Colorado. The shortstop is a staggering 9 for 11 with two homers, four RBIs and five runs in those meetings. He's also 3 for 6 with two walks against Colorado's scheduled starter, Jorge De La Rosa.
Stephen Strasburg (7-7, 3.55 ERA) hasn't won since facing the Rockies on July 1. He held them to one run and five hits with eight strikeouts in 7 2-3 innings of a 7-1 victory, but is 0-1 with a 3.66 ERA in three starts since.
The right-hander struggled early in his latest outing Friday. He surrendered all of Milwaukee's runs in the first three innings before leaving after the seventh with nine strikeouts in a 4-2 defeat.
Improving on the road may be a tall order for Strasburg, who is 1-5 with a 4.92 ERA in nine away starts, including 0-2 with a 6.35 ERA in his last three.
He's taking the mound at Coors Field for the first time since allowing three runs with eight strikeouts in six innings of a 4-2 loss June 25, 2012.
The Rockies own the NL's worst record and are trying to avoid matching a season-worst eight-game slide from May 28-June 6.
Turning to De La Rosa (10-6, 4.39) may help since the left-hander is 4-0 with a 3.48 ERA in five starts after compiling an 8.20 ERA and 0-3 record over his previous four.
He's allowed one run in six innings in each of his last two, but the bullpen wasted his effort Friday by surrendering three runs in two innings of a 4-2 loss at Pittsburgh.
De La Rosa allowed three runs in 5 1-3 innings of a 5-1 defeat in his most recent home meeting with the Nationals on June 12, 2013. He was much better in Washington 11 days later, yielding two runs in six innings of a 7-6 win.
Josh Rutledge is 6 for 15 (.400) in the last four games, starting at shortstop in each of the previous three due to a left hip flexor strain that landed Troy Tulowitzki on the disabled list. Rutledge tripled for one of his two hits Tuesday and is 3 for 5 with a double off Strasburg.