Stephen Piscotty had three hits, including a homer, and drove in a career-high five runs and Leake pitched seven scoreless innings as the Cardinals salvaged the finale of the three-game series.
"It is a good win. We needed that," said Piscotty, who returned to the lineup Monday after missing games Saturday and Sunday with a sore knee. "Leake did a tremendous job on the mound. It felt good to get that."
The Nationals scored 22 runs in the first two games of the series, but Leake (1-1) gave up just four hits with seven strikeouts and no walks to lift the Cardinals, who had lost three in a row and six of seven.
"You can't take anything away from Leake," Baker said. "We had him on the ropes and then the pickoff. His ball was moving. His cutter was really working today and his sinker and he would throw an occasional change-up and breaking ball."
Leake had lost his last four decisions against Washington but retired 19 batters in a row at one point.
"It is ideal. It is what you ask for in the starting pitcher," Leake said of halting the Cardinals slide. "They were swinging the bats well. They are a threat at any point."
Leake struck out Jayson Werth for the final out in the seventh with two runners on as the outfielder watched a 92 mile-per-hour fastball catch the outside part of the plate.
"What an amazing job all the way around," Mike Matheny, the Cardinals manager, said of Leake. "What a great day. Seven shutout innings against this team. The way he did it just seems to be a carryover from what we have seen so far this spring."
Trevor Rosenthal gave up an RBI single in the eighth to Adam Eaton as the Nationals trimmed the lead to 3-1 with one out. Reliever Matt Bowman, from nearby Chevy Chase, Maryland, got one out on a fielder's choice and University of Maryland product Brett Cecil retired Bryce Harper on a liner to third for final out of the frame.
"It got a little hairy there," Matheny said. "Cecil, we know, is going to get those big outs."
Piscotty then hit a three-run homer in the ninth off Joe Blanton to give the Cardinals a 6-1 lead.
"Stephen was the offensive story. What a great day for him all the way around," Matheny said. "We have a long way to go. Days like this are going to happen. We are a good team. We are expecting good defense."
Losing pitcher Scherzer (1-1) allowed three runs (one earned) and four hits with 10 strikeouts in six innings. He struggled with his command, throwing three wild pitches and hitting a batter.
The Cardinals scored two in the fifth to take a 3-0 lead. Matt Carpenter drove in a run on a sacrifice fly and Piscotty had an RBI single to left. Piscotty gave the Cardinal a 1-0 lead in the first as he slammed a 95 mile-per-hour fastball from Scherzer for an RBI double.
"Piscotty beat us by himself today," Baker said. "Heckuva day for Leake and Piscotty. He's a very good hitter and he's not going to stay cold for long."
The Nationals ruined a golden chance in the first. Eaton led off with a double and Anthony Rendon singled him to third, but Rendon was picked off and Leake retired Harper and Daniel Murphy. Eaton and Ryan Zimmerman had two hits.
"What a jam that was," Matheny said of the first inning pickoff. "That is a game-changing play for sure" as Carpenter tagged out Rendon.
NOTES: Cardinals 1B Matt Carpenter was back in the lineup after back stiffness kept him out of the starting lineup Tuesday. ... Washington put INF Stephen Drew (right hamstring strain) on the 10-day disabled list and called up INF Grant Green from Triple-A Syracuse. The Nationals will be the fourth major league team for Green, a first-round pick in 2009 by the Oakland A's. ... St. Louis RHP Michael Wacha (1-0, 1.50 ERA) will start on Friday in New York against the Yankees and RHP Masahiro Tanaka (0-1, 11.74 ERA). ... Nationals RHP Stephen Strasburg (1-0, 3.21 ERA) will face Phillies RHP Aaron Nola (1-0, 4.50 ERA) on Friday in Washington.