Dallas led by nine points entering the fourth quarter, but Phoenix made four 3-pointers in the first three minutes to pull to 53-52. The Wings scored the next 12 points to seal it as the Mercury went scoreless for nearly six minutes.
Arike Ogunbowale and Allisha Gray each added nine points for Dallas (2-5), which has won two straight. Thornton had eight points and seven rebounds in the first half to help Dallas build a 33-27 lead.
Leilani Mitchell led Phoenix (2-5) with 12 points and four 3-pointers. Brittney Griner added 11 points and blocked four shots to move into a tie with Lauren Jackson for third on the WNBA career list with 586.
DeWanna Bonner, the WNBA's scoring leader at 23.8 points, and Griner combined to make just two of their first 15 shots as Phoenix trailed 43-31. Bonner finished with nine points.