The Dodgers, who lead the National League Wild Card standings, sit just 1.5 games behind the San Francisco Giants in the National League West division standings.
"All three of my pitches worked early on and felt good all the way through," Urias told reporters. "I went as long as I could."
Second baseman Trea Turner struck out in the Dodgers first at-bat in the bottom of the first. Muncy hit his 29th home run of the season two pitches later. The Dodgers first baseman hit the 405-foot solo shot off Braves starter Drew Smyly.
Smith followed with another solo homer in the Dodgers' third at-bat of the second. That 383-foot blast went 104 mph to left field, according to Statcast.
Betts gave the Dodgers a 3-0 edge with another solo homer to lead off the bottom of the third. That homer off Smyly traveled 378 feet to left field and went 103 mph off Betts' bat.
Dodgers third baseman Justin Turner singled in the next at-bat. Seager hit a 400-foot, two-run homer to left field two at-bats later.
Braves right-fielder Jorge Soler and first baseman Freddie Freeman answered with back-to-back home runs in the top of the sixth. Outfielder Adam Duvall added a 395-foot solo homer in the top of the seventh, but the Braves could not complete their rally.
Dodgers relief pitcher Blake Treinen allowed two hits and no runs over the final 1 1/3 innings to earn his fifth save of 2021.
Smyly allowed nine hits and five runs over 4 2/3 innings to drop to 9-4 this season. Duvall went 2 for 4 in the loss. Muncy, Smith and Justin Turner recorded two hits apiece for the Dodgers.
"It was great," Dodgers manager Dave Roberts said. "The homers, the at-bats, taking walks when we needed to. I thought we did a nice job against Smyly."
The Dodgers (83-49) host the Braves (70-60) in the second game of the series at 10:10 p.m. EDT Tuesday at Dodger Stadium.