The fifth and deciding game will be played Thursday in Washington. The winner advances to the NL Championship Series to face the Los Angeles Dodgers.
Strasburg shut down the Cubs a day after he continued to experience flu-like symptoms that began last week. The right-hander was not expected to start for the Nationals, who faced elimination after Game 4 was pushed back to Wednesday due to rain.
But after reporting to Wrigley Field on Wednesday morning feeling better after receiving antibiotics and a fluid IV for the past two days, Strasburg was dominant in keeping the Nationals alive.
Strasburg, who held the Cubs without a hit for 5 2/3 innings in Game 1 of the series, allowed just three hits and walked two. Strasburg struck out the side three different times to silence the Cubs.
With the Nationals clinging to a 1-0 lead in the eighth, Taylor blew the game open with the first postseason grand slam in Nationals' franchise history off Cubs closer Wade Davis. Davis entered the game with two outs in the inning after reliever Carl Edwards, Jr. walked a pair of hitters to load the bases.
Davis took over and surrendered the home run, which drifted into the right field bleachers with the wind blowing in.
The Nationals took a 1-0 lead in the third inning. After Trea Turner doubled off Cubs starter Jake Arrieta with one out and advanced to third on a wild pitch, Arrieta struck out Jayson Werth to get within an out of getting out of the inning. But following a Bryce Harper walk, Cubs shortstop Addison Russell booted a Ryan Zimmerman ground ball, which allowed Turner to score.
The Nationals loaded the bases in the fourth inning with Arrieta laboring. Arrieta, who took the loss, allowed an Anthony Rendon lead-off double and then issued walks to Taylor and Turner. But Arrieta struck out Werth looking to wiggle out of trouble.
Arrieta allowed two hits and no earned runs over four innings, walked five and struck out four.
NOTES: Nationals SS Trea Turner snapped an 0-for-13 drought with a one-out double off Jake Arrieta in the third inning. The hit was the first of the NLDS for the Nationals' leadoff hitter. ... Cubs manager Joe Maddon tweaked his lineup prior to Game 4 after the Nationals allowed RHP Stephen Strasburg would start in place of RHP Tanner Roark. Cubs RF Jason Heyward was inserted in the No. 7 hole in place of OF Kyle Schwarber, who had been scheduled to start against Roark. ... Nationals manager Dusty Baker said Roark could be a candidate to pitch in Game 5 on Thursday. ... Cubs LHP Jon Lester entered the game in the fifth inning and made his first relief appearance since Game 7 of the 2016 World Series.