The veteran right-hander has beaten the Nationals twice without allowing an earned run and will face them again Monday night at Dodger Stadium.
The Nationals (77-58) own the NL's best record and are atop the East while the West-leading Dodgers (77-60) are one game behind them in the race for the top seed entering this three-game set.
Exactly one month ago, Hernandez (8-9, 3.81 ERA) limited Washington to one unearned run over eight innings to earn a 2-1 victory in his final start with Philadelphia. He also beat the Nationals on May 4, pitching 7 1-3 innings in a 1-0 win.
He was acquired Aug. 7 by the Dodgers, and has gone 2-1 with a 3.52 ERA in four starts with his new club. Hernandez allowed three runs over six innings to get credit for Tuesday's 9-5 win at Arizona.
There is strong competition behind Clayton Kershaw, Zack Greinke and Hyun-jin Ryu in the Dodgers' playoff rotation for a possible fourth starter. Los Angeles still has work left to clinch the West with a 2 1/2-game lead over San Francisco.
''It's always good for us,'' manager Don Mattingly said. ''We're in position to control our own destiny.''
Hernandez has faced Denard Span more than any Nationals hitter, with the center fielder 11 for 38 against him. Span finished August with 40 hits as he batted .328 in the month.
One Washington hitter on a roll is Bryce Harper, who went 6 for 11 with three homers over the weekend as his club took two of three in Seattle.
Harper, who is 1 for 3 against Hernandez, notched his fifth career multihomer effort in Sunday's 5-3 defeat.
''I don't think he's done anything different I just think he's getting stronger,'' manager Matt Williams said of Harper, who missed 57 games with an injured thumb.
''His hand is getting stronger. It allows him to stay back and calm and keep his body down a little bit. We've seen that over the last couple weeks. It's getting there.''
Los Angeles avoided a three-game sweep with Sunday's 7-1 victory at San Diego. Adrian Gonzalez had four hits and Juan Uribe drove in two runs in his first game since Aug. 15 after being out with a strained right hamstring.
The Dodgers improved baseball's best record in games against left-handed starters to 23-11 by beating Eric Stults. They will face another one Monday in Gio Gonzalez.
Gio Gonzalez (6-9, 3.86) is enduring the longest winless drought of his career, going 0-5 with a 4.38 ERA in his last nine outings. He hasn't received a decision in his last three, giving up three runs in six innings Tuesday in a 4-3 loss to the Phillies.
He is 0-1 with a 1.50 ERA in two career starts against the Dodgers, limiting Adrian Gonzalez to two hits in 12 at-bats.
These teams each scored 10 runs as Washington took two of three at home May 5-7. The Nationals have dropped 19 of their last 23 at Dodger Stadium.