Hudler scored 3:14 into overtime as the Flames avoided joining Edmonton in the Western Conference basement, defeating the Oilers 2-1.
There was a hectic end to an otherwise rather sedate affair.
Edmonton tied the game with 10.1 seconds left to spoil rookie goalie Reto Berra's bid at his first career shutout. With their own goalie pulled, Oiler David Perron was able to send the puck behind the Calgary goalie from the side of the goal to Taylor Hall, who shovelled it into a wide-open net.
The Flames got their revenge in extra time as a shot from the point ticked off the stick of Ryan Nugent-Hopkins and past defender Justin Schultz to Hudler on the doorstep, who potted his eighth of the year.
The Flames' centre wasn't originally going to play in the game.
"I didn't travel with the team last night because I felt a little sick and they didn't want me on the plane because it's going around, so we didn't want to get many guys exposed," Hudler said. "I got up this morning and I talked to the trainers and we booked a flight after lunch. We weren't sure, but if I'm travelling I want to play."
Flames coach Bob Hartley said it was fitting Hudler got them over the final hurdle.
"Jiri deserves lots of credit, he was sick, he left the game last night and went home sick," he said. "He was sick all night and flew in this afternoon and it was a gutsy effort."
Lee Stempniak scored in regulation for the Flames (11-14-4) who have won three of their last four games.
"I was very, very impressed with our team," Hartley said. "We battled for 60-plus minutes. Even when they got the tying goal, I could feel the disappointment on the bench, but I told them, we played so good, just keep going."
Berra earned his fourth career win with a 30-save performance.
"I'm really happy that we had the win," he said. "It was really close and right after the goal you're frustrated, especially as the goalie. But you have no time to think about that or to be frustrated, the next shot is the most important. I'm happy because I think I did well, they had two or three good chances in OT. I felt I was good on the puck and square and it was a good feeling for the whole team that we won this one.
The Oilers (10-18-3) continue to have trouble gaining much traction at home, slipping to 4-9-1 at Rexall Place.
"It was not the best effort from us," Hall said. "It was nice to score that goal late. It was a huge rush and a boost for the team to send it into overtime. They got a bounce in overtime and put it in. They played their system well and it seemed like they were just waiting for us to turn over pucks and unfortunately we kept doing that."
Oilers coach Dallas Eakins said the constant turnovers his team made were the difference between a 2-1 loss on Saturday and an 8-2 win over Colorado on Thursday.
"It was disappointing in that regard," he said. "It was almost like we couldn't help ourselves with our turnovers.
"Sometimes when you get eight in a game, it starts to seep into your game that you think you are going to have your way every shift."
It took 16 minutes before the game's first goal.
Edmonton coughed up the puck at the Flames' blueline and Oilers defender Andrew Ference got pinched against the boards to allow a two-on-one break, with Stempniak opting to shoot it himself to beat goalie Devan Dubnyk with a high shot glove-side. It was Stempniak's sixth goal of the season.
The Oilers came close to tying it with just six seconds left in the first, but a power play shot by Perron hit the post behind Berra.
Much of the first-period play favoured Edmonton, as the Oilers outshot Calgary 12-6.
The Flames had a three-on-one break five minutes into the second period, but Dubnyk was able to come across in time to make a pad save on Lance Buoma.
Berra had to be sharp to keep it scoreless in the second as the Oilers were buzzing late in the period and Ales Hemsky redirected a Ference shot while on his knees in the slot that the Flames' goalie was quick to get across and stop.
The shots closed to 22-16 for Edmonton after 40 minutes.
Both teams are off until Tuesday when the Oilers will play the fourth game of a five-game homestand against Carolina, while the Flames return home to entertain Boston.
Notes: It was the second of five games between the provincial rivals this season. Edmonton won the first match-up 4-2 on Nov. 16, after trailing 2-0 after 40 minutes… Defenceman Jeff Petry made his return to the lineup after being a healthy scratch during the Oilers 8-2 win over Colorado on Thursday. Corey Potter came out to make room. However, Petry left the game early in the second period and did not return after being hammered into the post between the boards and the bench by David Jones… Former Oiler defenceman Ladislav Smid made his first return to Edmonton since a rare trade between the two teams that sent him to the Flames earlier this season. The Oilers picked up prospects Roman Horak and Laurent Brossoit. Smid played seven seasons in Edmonton… The injury-riddled Flames had some good news when centre Joe Colborne returned to the lineup after missing Friday's loss to the Avalanche with the flu. Winger Brian McGratton also came back from a lower body injury… The Flames remained without forwards Curtis Glencross (knee) and TJ Galiardi (back spasms), centre Sean Hudle (fractured foot) and defenceman Dennis Wideman (fractured hand)… Edmonton was still without face-off specialist Boyd Gordon (shoulder), goalies Ilya Bryzgalov (concussion/whiplash symptoms) and Richard Bachman (lower body) and forward Tyler Pitlick (knee).