Betts went 1 for 2 with two runs scored, two walks and an RBI in the 3-2 victory at Dodger Stadium. The five-time All-Star missed 16 games in August due to hip issues, but returned to the Dodgers lineup last week.
"We are a lot better team when he is out on the field healthy," Seager told reporters. "What he can do all around, he showed.
"He made a good catch, ran the bases well and hit a homer. We are a lot better when he is out there."
The Dodgers win and a San Francisco Giants loss Tuesday brought Los Angeles to just 0.5 game behind their rivals for first place in the National League West. The Dodgers lead the National League Wild Card standings by 13 games.
Braves center fielder and former Dodger Joc Pederson hit a 398-foot, leadoff homer in the top of the third for the first run of the game. Catcher Travis d'Arnaud doubled the Braves lead with an RBI double in the top of the fourth.
Betts responded with a leadoff homer in the bottom of the same frame, hitting the first pitch from Braves starter Charlie Morton to left field for a 381-foot solo shot.
Dodgers outfielder Chris Taylor drove in the tying run with an RBI sacrifice fly in the bottom of the seventh.
Relief pitcher Blake Treinen replaced Dodgers starter Walker Buehler in the top of the eighth. Treinen struck out all three batters he faced. Betts then led off the bottom of the eighth with a walk. Third baseman Justin Turner flew out to right field in the next at-bat.
Seager then stepped to the plate and smacked a 2-2 fastball to center field. Betts got a great jump off first, raced around second and third and slid over home to score the winning run.
Dodgers closer Kenley Jansen retired Austin Riley, d'Arnaud and Dansby Swanson in order in the top of the ninth to earn his 30th save of the season.
Seager went 1 for 3 with an RBI and a walk in the win. Buehler allowed four hits and two runs over seven innings. Morton allowed three hits and one run in six innings.
"[Betts is] a special player and does a lot of things really well on the field," Buehler told reporters. "Corey [does] the same thing. We had a big play from two of our big-time players."
The Dodgers (84-49) next host the Braves (70-61) in the final game of the series at 6:10 p.m. PDT Wednesday at Dodger Stadium.