Ryan Nugent-Hopkins led the way offensively with a goal and two assists, while Jesse Puljujarvi and Leon Draisaitl rounded out the rest of the scoring. Cam Talbot made 32 saves in the losing effort.
The Oilers went 1-for-2 on the power play and 1-for-3 shorthanded. They won 53 percent of the faceoffs.
"Tonight we cheated on the first one, we're going for offence and we cheat," said Oilers Head Coach Todd McLellan, referring to the first power-play goal against.
"The second one, we shouldn't have been penalty killing."
Jonathan Toews, Alex DeBrincat and Kane all had five or more shots on goal.
Glass was made aware he'd be starting in his home province early in the morning when the Blackhawks entered Edmonton. He was tested early and often, stopping his first career shot against - an Andrej Sekera slapper from the point. The netminder followed that up by stymying Connor McDavid's far-side wrister off the rush.
"It feels pretty good," said Glass post-game. "In the first period, it felt nice to touch the puck, get some saves early and it felt kind of routine after that."
Talbot, making his 214th career NHL start, made an unbelievable save on Brandon Saad at the other end. Talbot slid across to stop Saad's feathered deflection, getting enough of the puck then making a quarter turn for it to pop out of his equipment.
The Oilers held most of the momentum throughout the opening period. They had an abundance of chances: the top line caused an offensive flurry that they failed to close, Michael Cammalleri dinged the post and Draisaitl broke in uncontested but his backhand 5-hole attempt was squeezed by the pads of Glass.
"We had numerous chances to take the lead and take some of the will away from them and they stuck around," said McLellan. "We were able to come back and earn the point but it was a frustrating night for our team and for some individuals."
It wasn't until the Oilers first power play of the night, manufactured by the second unit, when they would beat the visiting goaltender. Nugent-Hopkins fired a wrist shot from the left circle and Puljujarvi was in the right spot to deposit the rebound at 14:26. It was the Finn's first goal at Rogers Place this season and eighth of the campaign. Nugent-Hopkins and Oscar Klefbom registered the assists.
Chicago tied it up with just under a minute remaining in the period. Kane cruised into the slot, corked a wrist shot that Talbot couldn't catch and Ryan Hartman banged home the rebound.
The Oilers came out in the middle stanza with their foot on the pedal. Ryan Strome had a chance at the side of the net but he chose to pass the puck out front, having it intercepted by a Blackhawks player. Later, McDavid circled the offensive zone and centred a pass that neither of his linemates could get to.
The early energy from the Oilers drew a Saad hooking minor, giving Edmonton their second man-advantage of the evening. The second unit almost got their second of the night. Strome fired a one-timer that hit the post then trickled past Glass but was swatted clear of the crease.
"Maybe we could have got more second and third opportunities but he (Glass) did stand tall in there for them," said Nugent-Hopkins of the Oilers offence. "We found a way to break him at the end but it's disappointing we couldn't get that second point."
As Chicago fended off the Oilers, they were given a chance to take the lead after Darnell Nurse was called for holding while trying to disrupt Richard Panik on a breakaway. Edmonton failed to clear the zone while killing the penalty, allowing DeBrincat some room up the middle. He released a shot 5-hole that beat Talbot to give the Blackhawks a 2-1 lead at 14:06 of the second, which they would take into the final 20 minutes of play.
Chicago added an insurance marker in the third, courtesy of former Oilers defender Jordan Oesterle. He ripped a wrist shot on the power play that dinged the post and banked off Talbot's back to cross the line, giving the visiting squad a 3-1 lead. The goal was Oesterle's first of his career.
"Too many men on the ice, completely under control, didn't need to have it," said McLellan of the bench minor the Oilers received to cause Oesterle's goal. "Lost a draw, they shot it past guys and Talbs was a bit screened."
But Edmonton did not relent. The home squad responded with two late goals in under three minutes.
First, it was Nugent-Hopkins getting Edmonton within one with a wrist shot from the point that Brent Seabrook got a piece of with his glove. The redirection eluded Glass, giving Nugent-Hopkins his 15th of the campaign.
Then Draisaitl hammered home a rebound on the doorstep, tying the game up 3-3 with 55 seconds remaining.
"That push at the end for us is something we can build on," said Nugent-Hopkins.
Kane scored the game-winner just 50 seconds into overtime to give the Blackhawks a 4-3 victory.
"They had the puck the whole time in overtime and he (Kane) made a great play and great move," said McLellan. "He's done that to many, many players in the NHL that are very skilled and talented like Leon is."
The Oilers host the Winnipeg Jets on Sunday in the final game of 2017. Puck drop is at 5:00 p.m. MST.