Kendrick also tripled in the 6-2 victory -- finishing a double short of a cycle -- Tuesday at Busch Stadium in St. Louis.
"There is no panic," Nationals manager Chip Hale told reporters. "Once the game was over Monday, it was a new one Tuesday. You win, you start from zero tomorrow.
"There is definitely no panic. These guys have a lot of fun. Obviously winning is a lot more fun than losing."
The Nationals took a 1-0 lead on an Asdrubal Cabrera sacrifice fly in the top of the second inning. St. Louis tied the game on a third inning fielding error.
Juan Soto began the fourthinning with a strikeout before Kendrick stepped into the box. He fell behind 0-2 in the count against Cardinals starter Miles Mikolas. Kendrick then smashed a 79-mph curveball over the center field fence for his 16th homer of the season. The 404-foot shot left the field in 5.1 seconds, according to Statcast.
Victor Robles gave the Nationals a 3-1 cushion with an RBI single in the top of the sixth frame. Cardinals pinch hitter Jose Martinez struck out in the bottom of the sixth inning, but Tommy Edman scored on a throwing error during the sequence.
Robles recorded another RBI for the Nationals in the eighth frame, plating Cabrera on an RBI single. Yan Gomes scored Robles in the same inning with an RBI double for a 5-2 lead.
Soto plated the final run of the game with a sacrifice fly for the Nationals in the top of the ninth inning. Hudson entered the game in the eighth inning. He struck out DeJong in his first exchange, before allowing a Yadier Molina double. Hudson escaped the inning by getting Edman to fly out before striking out Harrison Bader. Hudson did not allow a hit in the ninth inning.
Robles went 2 for 3 with two RBIs and a run scored. Gomes went 2 for 3 with an RBI and a walk. Mikolas allowed eight hits and three runs in six innings for the Cardinals. Nationals starter Patrick Corbin earned his 13th win of the season after allowing five hits and two runs in six innings. Corbin also had 11 strikeouts.
The Cardinals host the Nationals in the final game of the series at 1:15 p.m. EDT Wednesday in St. Louis.