Before the game, Hanrahan received several text messages from his former Nationals teammates telling him, "Good luck today."
The game resumed with Washington winning, 11-10, in 11 innings.
Hanrahan, who pitched the top of the 11th on May 5, ended up with his first victory of the season even though he was in Philadelphia with the Pirates. Last week, Hanrahan was part of a four-player trade that sent outfielder Nyjer Morgan and left-hander Sean Burnett to Washington.
Hanrahan, still 0-0 with Pittsburgh, improved to 1-3 this season.
"I'm happy I [received] the win and to see the Nationals get another victory in the win column," said Hanrahan, who was one of seven Nationals players to participate in the May 5 game but are no longer on the 25-man roster.
When play resumed at 7:08 p.m. ET, LaTroy Hawkins started for Houston and the Nationals were able to score within seven minutes.
With Elijah Dukes no longer on the roster, Morgan pinch-ran for Dukes. Willingham came to the plate and singled to left to put runners first and second.
Josh Bard, pinch-hitting for Hanrahan, hit a routine ground ball to second baseman Jeff Keppinger, who was able to get the force at second, but shortstop Miguel Tejada threw the ball over first baseman Lance Berkman's head, which allowed Morgan to score.
According to the Elias Sports Bureau, the last time a team completed a walk-off win in an opposing stadium was 1975. The Yankees' game against the Twins at Shea Stadium (while Yankee Stadium was being renovated) on July 12 was suspended in the middle of the 14th inning with the score tied at 6.
The game resumed on July 19 at Minnesota's Metropolitan Stadium. After the Twins scored a run in the top of the 16th inning, the Yankees prevailed in the bottom half of the inning on back-to-back, two-out RBI singles by Graig Nettles and Lou Piniella.