Ryan Smyth scored his second goal of the game during a power play at 3:18 of the extra session to net the actual game-winner.
Just 16 seconds earlier, it appeared that Fernando Pisani slid the puck past Khabibulin's glove and barely over the goal line. But the goal was disallowed after a video review.
"We battled through a little adversity," Smyth said. "That's what you have to do. You have to fight through adversity at this stage of the game and find ways to win. We have a great character team."
Even Chicago coach Trent Yawney believed Pisani had won it.
"I thought it was in," Yawney said. "The guys were saying it was. I guess (Khabibulin's) glove made it inconclusive."
It was the second straight game in which the Oilers had a key goal disallowed. In a 2-1 shootout loss at Minnesota on Thursday, an apparent short-handed tally by Michael Peca early in the second period was waved off.
"Flukey goal, their third goal, but nonetheless they pushed us into overtime, Smyth said. "We'll take the win."
Smyth also had an assist as the Oilers improved to 91 points and moved into sixth place in the Western Conference, four points ahead of ninth-place Vancouver.
"He was unbelievable again," Edmonton coach Craig MacTavish said of Smyth. "He's more dominant now than at any point in his career. It couldn't come at a better time.
"This win is huge for us emotionally. It would have been very demoralizing for us to come out of here with anything less than two points."
Hemsky and Pisani had power-play goals for Edmonton, which was 3-for-5 with the advantage. Roloson made 23 saves in his 16th straight start since arriving in a trade from Minnesota on March 7.
Eleven of Chicago's last 12 games have been decided by one goal, with the Blackhawks winning just four. For the season, they are 12-26 in one-goal games.
"Twenty-six one-goal losses, that's really frustrating," Calder said, "especially when we battle so hard."
Khabibulin made 35 saves, including several on point-blank chances.
Smyth opened the scoring 6:50 in during a delayed penalty call against Chicago.
After Khabibulin's pad save on Shawn Horcoff's drive, Smyth backhanded the rebound in between the goalie's legs.
Vrbata's power-play goal with 37 seconds left in the first period tied it 1-1. He fired in a screened shot from midway between the left circle and the point.
The Oilers took a 3-1 lead in the second with a pair of power-play goals.
Hemsky gave the Oilers a 2-1 lead during a 5-on-3 power play at 8:14. Khabibulin stopped Smyth's goal-mouth deflection of Jarret Stoll's shot from the point, but Hemsky popped in the rebound from the left side of the crease.
Pisani made it 3-1 with 4:07 left in the period. Bell's power-play goal at 4:06 of the third cut it to 3-2.
- The Blackhawks hope forward Tuomo Ruutu will return to the lineup next Tuesday at Minnesota. Ruutu has missed 34 games with severed tendons in his right ankle. Ruutu, sidelined for 25 games with a back injury earlier this season, has appeared in only 11 games.
- Smyth extended his point streak to eight games. He has five goals and six assists during the span.
- Calder's goal was his career-high 22nd.