''We always take it upon ourselves to have a good defensive game because we know that's what creates our offense,'' Hayes said. ''We definitely wanted to work hard on the defensive end tonight.''
The Dream (13-5) have won two straight and four of five, retaining their 4 1/2-game lead over Indiana in the Eastern Conference. The Fever beat Tulsa 78-76.
Atlanta's defense held Connecticut to 39 percent from the field, dropping the Sun to 1-7 this year when they finish under 40 percent.
''We did a good job defensively on certain players, limiting their shots,'' Cooper said. ''Each game is important for us because it's leading us on the path to where we want to end up, and that's a championship.''
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 and dropped into a tie for third place in the East with Chicago, 5 games behind Atlanta.
''I made a personal goal to play harder in the second half and had the support of my teammates,'' Ogwumike said. ''But I think (the Dream) controlled the tempo because they played like a team, they celebrated together, and that's one thing that we're trying to do consistently. They did it for 40 minutes. We did it for about 25 minutes.''
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.
Connecticut's 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.
''She's like a banger down there,'' McCoughtry said. ''She likes to be tough. We just had to body her up a little bit. We gave Katie a couple of 3s that of course we didn't want to give up, but I think we picked it up in the second half defensively.''
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.