Sancho Lyttle added 13 points and Armintie Price had 10 for the Dream (17-14), who have won five of their last six.
Lauren Jackson had 14 points and nine rebounds and Camille Little added 13 points and eight boards for the Storm (13-15), who have already secured their WNBA-record ninth consecutive playoff berth.
Seattle pulled to 55-54 on a 3-pointer by Sue Bird early in the fourth quarter. However, Atlanta went on a 13-0 run to regain control and finished with a 22-7 spurt.
The Dream were swept by the Storm in three games in the WNBA Finals in 2010, but have won the four regular-season meetings since.
Trailing by 16 points early in the second half, Seattle went on a 19-6 run to pull to 49-46 on a three-point play by Jackson with 2:13 left in the third quarter. The Storm trailed 53-49 going into the final period as Jackson had 10 points in the period and Little scored nine.
McCoughtry, who didn't attempt a shot in the first quarter, was 6 for 6 from the floor and had 14 points in the second quarter as Atlanta took a 37-25 halftime lead.
McCoughtry scored all but two points during a 16-6 run that gave the Dream a 37-21 lead late in the quarter. DeSouza had eight of her 10 first-half points in the first quarter.
Seattle, which had shot 60 and 58 percent in consecutive weekend victories over Tulsa, made just four of its first 14 shots — missing four 3-pointers — and trailed 19-14 at the end of the first quarter.
The Storm, who have six games remaining, play at Indiana on Wednesday night and then conclude their four-game road trip at San Antonio on Friday. Atlanta is at Washington on Friday in the first of three road games to end the regular season.
More Sports Headlines
Snohomish mixed martial artist returns to her first love Mariners beat Twins 4-3 in 11 innings Charles scores 29 points, Liberty beat Storm 78-62 4:49 p.m. Park wins Women's British Open, captures 4th different major 4:38 p.m. Perry wins 2nd straight Champions Tour's 3M Championship 4:33 p.m. Merritt shoots 67 to win Quicken Loans National by 3 shots 4:30 p.m. Triple Crown winner American Pharoah wins $1.75 million Haskell Invitational 4:25 p.m. Bills' Ryan names Incognito starting left guard 4:22 p.m.
Our new comment system is not supported in IE 7. Please upgrade your browser here.