Roneeka Hodges had 14 points, Shoni Schimmel added 13, and DeLisha Milton-Jones finished with a season-high 12.
A 3-pointer by McCoughtry midway through the second quarter sparked a 19-8 run that gave Atlanta (8-14) a 50-38 lead with 41 seconds left in the half.
Riquna Williams hit a 3 with 7:24 left in the third to pull Tulsa (10-13) within one, but the Dream scored 15 of the next 21 points to make it 69-59 about 3 minutes later and the Shock never threatened again.
Williams scored 35 points and Karima Christmas added 18 for Tulsa. The Shock have lost nine in a row, including five straight at home.
It was Atlanta's highest-scoring game of the season.