Leilani Mitchell added 13 points and hit three free throws with 19.9 seconds left to give the Mercury (9-8) a 67-63 lead. Bonner split a pair of free throws with 14.2 seconds left and Griner made two foul shots with 8.5 seconds left to seal the victory.
The Wings (5-14) had a brief rally late after missing their first 13 field-goal attempts of the fourth quarter and falling behind 62-56. Glory Johnson broke the field-goal drought with a driving layup and Theresa Plaisance followed with a 3-pointer to cut the deficit to one with 1:28 left.
Kayla Thornton had 16 points, Johnson added 15 and Plaisance scored 10 for Dallas.
The Mercury beat the Wings 69-64 in Phoenix on Wednesday.