Tampa Bay defenseman Matt Carle sent the puck from the neutral zone back into the Lightning defensive zone, where it went off Gudas and past a stunned goalie Ben Bishop into the net.
"I didn't think the first [goal] of the season was going to be like that," said Gudas, who hasn't scored a goal this season. "It bounced right in front of me, hit my [stick] shaft, my ankle and went straight in."
Tampa Bay coach Jon Cooper said it seemed as if the goal took place in slow motion.
"There's been some crazy goals the last year and a half, and that's one of them," Chicago coach Joel Quenneville added.
St. Louis got the game-winner from in-close, with Gudas getting his second assist of the season on the play.
"Obviously, that makes it a little better," Gudas said. "We got the win after all, even if something like that happens."
St. Louis, the Tampa Bay captain, also had an assist and moved past Neal Broten (923) for 93rd place on the career points list with 924.
Bishop stopped 38 shots.
Steven Stamkos scored a tiebreaking power-play goal as Tampa Bay (6-3-0) went up 5-4 at 17:31 of the third.
Stamkos finished with two goals and two assists. Carle, Nate Thompson and Victor Hedman had the other Tampa Bay goals.
The Lightning have beaten the defending Stanley Cup champion Blackhawks twice this season. Tampa Bay rallied from a 2-0, third-period deficit for a 3-2 shootout win in Chicago on Oct. 5.
"You look at the game that we stole in Chicago ... I don't think we stole tonight's," Cooper said.
Chicago (6-1-3) also got goals from Bryan Bickell, Marian Hossa, Patrick Kane and Andrew Shaw. Kane assisted on Shaw's goal, giving him five goals and 15 points in eight games against Tampa Bay.
Chicago took a 4-3 lead 93 seconds into the third on Shaw's in-close power-play goal. It was the first time the Blackhawks have scored during the third period since opening night.
Hedman's first goal in 41 games tied it at 4 at 11:03 of the third.
After blowing a two-goal lead, Stamkos gave Tampa Bay a 3-2 advantage at 17:21 of the second when he beat backup goalie Nikolai Khabibulin from the top of the right circle. It was just Khabibulin's second start in Tampa since helping the Lightning win the 2004 Stanley Cup.
Khabibulin made 19 saves.
"He'll be better going forward," Quenneville said.
Kane pulled the Blackhawks even at 3-3 on a breakaway goal with 1:07 remaining in the second.
Bickell cut the Blackhawks' deficit to 2-1 with a rebound goal with 11 minutes left in the second. The left wing has a goal in three consecutive games.
Chicago tied it at 2-all on Hossa's thigh-high re-direction 1:36 after Bickell scored. Hossa has 438 goals, which ties him for 62nd place all-time with Gary Roberts.
Tampa Bay took advantage of its first power play as Carle put the Lightning up 1-0 6:28 into the game. The Blackhawks entered with the NHL's third-worst short-handed unit.
Thompson stopped a 19-game goal drought to make it 2-0 during a short-handed 2-on-1 at 1:24 of the second.
There were a number of Hockey Hall of Famers with ties to the Blackhawks in attendance. Current Lightning broadcaster Phil Esposito spent time with former teammate Bobby Hull. Others at the game included Stan Mikita and current Blackhawks senior adviser Scotty Bowman. ... Stamkos has nine goals and 14 points in seven games against the Blackhawks. ... Chicago D Michael Kostka is expected to miss four to six weeks due to a lower-body injury. He was hurt during practice Tuesday.
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