Atlanta (16-9) increased its lead in the Eastern Conference to four games ahead of second-place Washington, which lost at New York. McCoughtry shot 10 for 16 from the field and Tiffany Hayes added a career high-tying 23 points in a matinee game at Philips Arena.
Kelsey Bone led Connecticut with 18 points and 13 rebounds, rookie Alyssa Thomas added 17 points and Chiney Ogwumike had 16, but the Sun (10-17) lost their fourth straight.
Atlanta got its first win under assistant coach Karleen Thompson. The Dream lost three straight after head coach Michael Cooper took a medical leave of absence July 21 after being diagnosed with tongue cancer. He had surgery last week.
McCoughtry shot just 34.7 percent in the previous four games. She said the team's skid wasn't related to Cooper's absence, but a failure of players taking care of business.
"We're professionals and no matter who we have on the bench, we still know how to play the game and sometimes coach ourselves," McCoughtry said. "Sometimes, Coach Cooper mostly sits on the sidelines and lets us figure it out anyway."
McCoughtry added seven rebounds and four steals, and forward Sancho Lyttle had 14 boards to help Atlanta outrebound Connecticut 41-32. Atlanta was outrebounded in every game during the losing streak.
"We haven't quite figured out how to impose our will," Sun coach Anne Donovan said. "Hayes is the one that really got away from us today, and their experience in the post is tough for our post players."
Atlanta led 44-41 at halftime and pushed it to 73-63 on Hayes' layup with 7:21 left. The Sun countered with eight straight points.
After Katie Douglas scored on a runner to pull Connecticut within 73-71, Thompson called timeout with 4:41 to go. The Dream scored six points out of the timeout and weren't threatened again.
Cooper had surgery on July 24, and team spokesman Brad Gust said Tuesday the timeline for his return remained at two weeks. Atlanta improved to 11-3 at home.
"It was a much-needed win for us, a good team win, with everything that is going on with Coach Cooper," Thompson said. "We wanted to get more points in the paint and attack the basket. They did well with that, our guards attacking from the perimeter and we controlled the boards."