Holik, who spent two largely disappointing seasons with the Rangers before the NHL lockout, gave the Thrashers their first lead of the night at 9:12 of the third period. He then won it after New York got even on Michael Nylander's power-play goal with 2:30 left in regulation.
Holik and Jim Slater scored 2:04 apart in the third period, and Marian Hossa broke out of a slump with a goal and three assists for the Thrashers, unbeaten in four games (3-0-1).
Adam Hall scored twice, and streaking Martin Straka added a goal for the Rangers, who dropped their second straight overtime decision following late, third-period rallies. New York has gone to overtime in three consecutive contests.
Kari Lehtonen shook off a soft first goal and followed up Saturday's shutout performance over Florida with a 30-save effort.