It was the Sun's their fifth straight loss.
Atlanta (11-16) opened on a 10-0 run and never trailed while holding Connecticut (12-15) to a season-low 18 first-half points.
Shoni Schimmel made four 3-pointers and scored 15 points for the Dream. Angel McCoughtry, who scored 33 points against the Sun on Sunday, was held to just three first-half points and finished with 11.
Atlanta's DeLisha Milton-Jones, the 40-year-old forward in her 17th season, matched the WNBA record for career games set by Tina Thompson (496).
The Dream led by 23 points midway through the third quarter. Connecticut used a 23-12 run, capped by Shekinna Stricklen's 3-pointer, to pull to 58-46 with 8:22 remaining.
Stricklen scored 14 points and Chelsea Gray had 12 to lead the Sun.