The Dream (13-5) have won two straight and four of five, pushing their Eastern Conference lead to five games over Connecticut, Chicago and Indiana.
Sun rookie Chiney Ogwumike, the WNBA's No. 1 overall draft pick, finished with 19 points and 12 rebounds and Alex Bentley added 19 points. Connecticut (9-11) has lost five of six.
The Sun's Katie Douglas, who began the game with 27 3-pointers in her last 10 games, hit her third 3 to cut lead to 51-43 midway through the third, but Connecticut never got any closer.
Atlanta went on a 16-6 run that included seven points and two rebounds by McCoughtry and Shoni Schimmel's 3-pointer.
In a nine-point loss at Connecticut on June 1, McCoughtry was suffering from a back injury and scored a season-low seven points on 2-for-14 shooting from the field.
Other than taking a fall and having to be helped up and escorted off the floor by trainers late in the second, McCoughtry seemed to have everything working in her favor this time. The WNBA's two-time defending scoring champion flashed her athleticism on a give-and-go underneath with Erika de Souza early in the third, putting back de Souza's missed layup attempt for a 47-34 lead.
Sun rookie Alyssa Thomas, the league's No. 4 overall draft pick, was 0 for 7 from the floor and went scoreless for the first time in 20 games this season.
Douglas finished with 16 points.
Sancho Lyttle and de Souza combined for 23 points and 14 rebounds for Atlanta.
The game was the first of three Dream home dates at Georgia Tech because of a scheduling conflict at Philips Arena.