Cooper missed Atlanta's past five games after being diagnosed with early-stage tongue cancer, and had surgery July 24. Team officials at the time said that Cooper, 58, was expected to miss about two weeks.
By winning eight of their past 12 games after a 4-11 start, the fourth-place Liberty (12-15) have pulled within five games of the first-place Dream (17-10) in the East, and New York took the season series against Atlanta 3-1.
Atlanta leads second-place Washington by 4 games, and Indiana by 4 1-2
If the playoffs began now, New York and Atlanta would meet in the first round.
Should Charles keep playing this way, New York's chances might be good against anybody. Over the past six games, she's averaged 22.7 points and 12.7 rebounds.
''It was a must win as far as a playoff berth; Atlanta already has a playoff berth, we don't,'' Charles said. ''So we just came in here with great intensity and energy. We were doing all the little things. We only had three turnovers in the second half and that was the biggest thing, I think.''
Atlanta this week qualified for the WNBA playoffs for the sixth consecutive season, but the Dream have dropped five of seven games.
Angel McCoughtry led Atlanta with 28 points, including four 3-pointrs, and Sancho Lyttle added 16 points for the Dream.
McCoughtry and Lyttle scored 10 points each in the first half and the Dream led 35-34.
In the third period, Charles scored 10 points, rookie Anna Cruz added nine and New York turned five Atlanta turnovers into 10 points as the Liberty put the game out of reach.
''In the six years that I have been here, every time it's the second half (of the season) where we play this way until the playoffs,'' Lyttle said. ''I don't know why, but I want to live to see the day that we don't.
''Maybe we've lost focus a little bit. Maybe we're playing like we know too much.''
Cooper, sporting atypical beard stubble on his face, told team officials he wanted to be present for the Dream's, ''Breast Awareness Health,'' initiatives, which on Sunday included acknowledging survivors of breast cancer.
The Dream wore pink uniforms for the annual event.
''I would like to thank all my friends and fans for all the well wishes and support,'' said in a statement released by the Dream before the game. ''I am excited to get back to coaching.''
It is unclear if Cooper will accompany the Dream on their upcoming four-game road trip, which begins Tuesday in Phoenix.