The Blackhawks ended a six-game winless skid in Nashville, winning for the first time here since Nov. 7, 2003. Havlat's empty-net goal with 54.8 seconds left came after David Legwand and Steve Sullivan had scored in a four-minute span, the last at 18:23, to pull Nashville within 7-6.
The Predators squandered a 4-3 lead when Chicago scored four straight goals starting at the end of the second period.
Rene Bourque scored shorthanded four minutes into the third, then added an assist on Bryan Smolinski's goal at 9:40. Smolinski assisted on Radim Vrbata's goal late in the third.
Martin LaPointe and Michal Handzus each added a goal and an assist for Chicago.
David Legwand had two goals and an assist for Nashville, and Ryan Suter had two assists.
Chicago, one of the NHL's original six franchises, came into this season trailing the series with the one-time expansion Predators 19-18-4 and had not won in six straight games in Nashville.
But Patrick Sharp tipped a sloppy pass from Sullivan to Bourque, skated up the left side and shot the puck through the legs of Tomas Vokoun for a 5-4 lead Chicago wouldn't lose.
Chicago goalie Nikolai Khabibulin stopped Scott Hartnell from in front of the crease twice in the next few minutes and helped a team that finished with the third-fewest points in the NHL last season start off with the victory.
Havlat got Chicago on the board after falling behind 2-0, scoring on breakaway in the first. He skated up and fed the puck to LaPointe at the mouth of the crease for an easy power-play goal at 14:24 of the second that tied it at four.
The Predators scored 28 goals in five exhibition games, and J.P. Dumont needed only 39 seconds into the regular season to show that pre-season performance wasn't a tease as he passed the puck to himself through Chicago defenceman Jassen Cullimore's legs and pushed it past Khabibulin.
But Nashville paid for putting most of its money toward offence by signing Jason Arnott and Dumont with five young defencemen. Captain Kimmo Timonen came in with 493 games' NHL experience compared to 418 for his five fellow defencemen.
Vokoun looked very rusty in his first game that counts since April 1. He missed the final eight games last season because of blood clots that kept him out of the playoffs.
Notes: Chicago went 13-1-4 last season when scoring four or more goals. ... Arnott's penalty in the second period put him at 1,001 penalty minutes in his career. ... Original Predators captain Tom Fitzgerald, who recently retired from the NHL after 17 years, dropped the ceremonial puck.