Warrick's free throw gave the Suns a 96-87 lead but the Mavericks scored seven in a row and closed within two on a layup by Dirk Nowitzki with 25 seconds remaining.
Grant Hill went to the foul line for Phoenix with 15 seconds left but missed both tries. Roddy Beaubois had two shots at tying the game in the final 4 seconds but missed them both.
The Mavericks lost for the sixth time in eight games.
Dallas had a 12-point lead with 4:43 to play in the third period but Phoenix closed the quarter on an 18-4 run.