Steve Cishek pitched 2 1/3 scoreless innings for his fourth save as the Cubs held on for a 6-5 win.
Chicago led 6-1 before Washington closed to within one on a three-run homer by Anthony Rendon in the sixth inning and a solo home run by Howie Kendrick in the seventh.
Cishek retired Rendon with a man on to end the seventh and allowed a single in the eighth before a 1-2-3 ninth.
Anthony Rizzo homered and Albert Almora Jr. had three hits for the Cubs, who took two of three from the Nationals and improved to 10-1-1 in their past 12 series.
Kyle Hendricks (4-4) retired the first 11 Washington batters and didn't allow a hit until Kurt Suzuki's single leading off the fifth, but gave up four runs and six hits in 5 2/3 innings. Hendricks had been masterful in May, allowing just one earned run over his past three starts (25 innings).
Washington starter Jeremy Hellickson (2-3) allowed three runs and four hits with three walks in three innings.
Yu Darvish (2-3, 5.14) starts the opener of a three-game series against former Cub Jake Arrieta and the visiting Philadelphia Phillies.
>>Blue Jays Down White Sox
Vlad Guerrero, Jr. hit another home run, Danny Jansen and Billy McKinney also connected and the Toronto Blue Jays beat the Chicago White Sox 5-2 on Sunday.
Guerrero has hit all four of his homers in the past six games and is 7 for 21 with nine RBIs during that span. The 20-year-old didn't homer in his first 13 games after making his debut in late April.
Guerrero's two-run drive broke a 1-all tie in the eighth inning. Jansen added a two-run homer in the ninth.
Jose Abreu drove in both runs for the White Sox.
Daniel Hudson (3-1) worked a scoreless seventh. Ken Giles gave up an RBI double to the first batter he faced, then got four outs for his 10th save.
Kelvin Herrera (1-3) took the loss.
Toronto starter Trent Thornton allowed one run and three hits in six innings. White Sox starter Reynaldo Lopez gave up one run and four hits in six innings.
The White Sox have not named a starter Monday night for the opener of a four-game series at Houston and likely will go with a bullpen day. Chicago was winless in seven games last season against the Astros, who will start RHP Brad Peacock (4-2, 4.01 ERA).
>>Ranger Outlast Cardinals in Extra Innings
Danny Santana connected for a pinch-hit home run in the eighth inning and then scoring the winning run in the 10th on a sacrifice fly by Nomar Mazara off Martinez that lifted Texas over the St. Louis Cardinals 5-4.
The Rangers rallied for two runs in the 10th and won for the fourth time in five games. The Cardinals dropped their fifth straight series and haven't won consecutive games since taking five in a row from April 27-May 1.
Dexter Fowler's solo homer in the ninth off Texas reliever Chris Martin made it 3-all.
The Cardinals went ahead in the 10th when Harrison Bader doubled off Jeanmar Gomez (1-0) and scored on a sacrifice fly by Paul DeJong.
Rougned Odor opened the Texas 10th with a single off Jordan Hicks (1-2), Santana walked and Calhoun had a tying single.
Hicks threw 39 pitches, the most of his two-year major league career.
DeJong drove in three runs for the Cardinals.
St. Louis starter Jack Flaherty gave up two runs on four hits with two walks and five strikeouts in six innings. Choo led off the first with a home run.
Rangers starter Drew Smyly sought his first win since Sept. 13, 2016, having missed the next two major league seasons following Tommy John surgery. He pitched four innings, allowing two runs in the first.
Michael Wacha (3-1, 4.93 ERA) will make his fifth career start against the Kansas City Royals on Tuesday and his first at home. Wacha is 3-1 with a 2.56 ERA against Kansas City.