Charles made a jumper with 50.9 seconds left for a 78-76 lead and Tanisha Wright sealed it with two free throws at 2.7.
New York (7-7) won its fourth straight game to complete a three-game road stretch. Charles became the seventh WNBA player to reach 3,000 career rebounds.
Brittney Griner scored 30 points and grabbed eight rebounds for Phoenix (5-6), which snapped a three-game win streak. DeWanna Bonner, the WNBA's leading scorer at 20.2 points coming in, was 3 of 13 from the field and finished with just nine points.
Griner scored 19 points in the first half to help Phoenix build a 41-40 lead. Nurse had 17 points for New York.