Tiffany Hayes, returning to the Dream (5-6) along with Aneika Henry after the pair missed five games while playing for Azerbaijan in a 3-on-3 tournament in Europe, added 12 points.
Jewell Loyd scored 12 points for Seattle (3-9), which has lost seven of its last eight. Alysha Clark, Ramu Tokashiki and Sue Bird added 11 each. Bird was just 4 of 15 shooting while leading scorer Crystal Langhorne was limited to five points.
The Storm, trailing by 15 late in the third quarter, rallied to within 63-62 on Clark's 3-pointer with 2:11 left. But McCoughtry turned in a three-point play and Sancho Lyttle, who grabbed 15 rebounds, had a pair of steals which led to four Dream free throws in the final 21 seconds as Atlanta finished on a 7-2 run.
The Dream announced before the game that they had traded guard Samantha Logic to San Antonio for the Silver Stars' 2016 second-round pick. Logic, selected No. 10 overall in this year's draft, appeared in four games, averaging 0.8 points.