EDMONTON — Evander Kane didn't have a team four months ago.

The controversial winger lugging around plenty of off-ice baggage was confident of an NHL return at some point. He just didn't know when or where.

Now he's filling the net alongside two of hockey's best.

Kane scored a natural hat trick during an electric six-minute span and Connor McDavid provided more magic with three assists in another dominant performance as the Edmonton Oilers downed the Calgary Flames 4-1 on Sunday to take a 2-1 lead in their second-round playoff series.

"I'm just happy to be part of this group," said Kane, who had his contract terminated by the San Jose Sharks in January before signing on in the Alberta capital. "Just trying to do my part."

McDavid, meanwhile, now has 23 points (six goals, 17 assists) through 10 playoff games this spring. The only players in post-season history with more over the same span are Wayne Gretzky (29 in 1983 and 25 in 1985), Mario Lemieux (25 in 1992) and Rick Middleton (23 in 1983).

"He's been on fire in the playoffs and has taken his game to the next level," Kane said. "He's not just doing it on the scoresheet. That's what's allowing him to really showcase his skill. He's physical, he's involved. A dominant force."

Leon Draisaitl, meanwhile, became the first player in league history to register four assists in a playoff period by setting up each of the home side's goals in a frantic second as the Oilers' top line combined for 10 points. Zach Hyman had the other goal for Edmonton.

"(Draisaitl) has been really good for our group," Kane said of a teammate sitting second behind McDavid in the overall playoff scoring race with 19 points despite battling through a suspected injury.

"Seems to find another level each and every night."

Mike Smith, who was briefly pulled from the action by the league's independent concussion spotter midway through the third after getting clobbered into the boards by Milan Lucic, made 32 saves for the victory.

Oliver Kylington replied for Calgary, while Jacob Markstrom allowed four goals on 34 shots before getting the hook behind a Flames group that has been outscored 8-1 since taking a 3-1 lead in the second period of Game 2. Dan Vladar made seven saves in relief.

"We lose the second period 4-0," Calgary defenceman Rasmus Andersson said. "We let one guy (McDavid) dominate."

The Oilers will look to take a 3-1 stranglehold on the best-of-seven Battle of Alberta — the first post-season meeting between the provincial rivals in 31 years — Tuesday night back at Rogers Place.

The first playoff contest in Edmonton to feature the Oilers and Flames since April 14, 1991, when Theo Fleury scored in overtime of Game 6 to spark a wild and memorable celebration, the Oilers exploded for those four goals in just over 12 minutes in the middle period, including Kane's second hat trick of the month.

Hyman opened the scoring with his sixth of the post-season 52 seconds after the restart following a 21-shot Edmonton first off a setup from Draisaitl and McDavid to ignite the crowd inside and outside the raucous, packed-to-the rafters arena.

"I think we had a lot of our younger guys that haven't been in this situation before (and) were a little bit intimidated by the atmosphere," Calgary head coach Darryl Sutter said.

Kane scored his first of the night at 6:58 off a feed from Draisaitl after the Flames turned the puck over at the offensive blue line.

He then pushed the lead to 3-0 on an outrageous McDavid rush after stepping past Calgary defenceman Noah Hanifin like he wasn't even there just 53 seconds later.

"We've let one guy beat us a few nights now," Flames forward Matthew Tkachuk said of McDavid's mastery.

"Back to the drawing board and figure out a way to stop him."

Smith made a great stop on a Johnny Gaudreau breakaway later in the period before also denying Tkachuk.

"Just trying to make saves for our group," said the 40-year-old goaltender, who spent a big chunk of the season out injured. "Trying to stay as poised as possible."

Kane completed his hat trick — the seventh-fastest in post-season history — with his 10th goal of the 2021-22 playoffs at 12:58 on a 2-on-1 with McDavid before fans littered the ice with headgear.

The 30-year-old Vancouver native is just the third Edmonton player to score three straight goals in a post-season game, joining Gretzky (1983) and Petr Kilma (1991).

After his contract was voided by San Jose, Kane signed on with his fourth NHL team despite plenty of questions about his past — from suspensions due to COVID-19 protocol violations, a bankruptcy and self-confessed gambling problems.

The biggest headlines from his personal life, however, were related to allegations of abuse lodged by his former wife, which were not proven in court. Kane has custody of the former couple's daughter.

"I didn't know Evander Kane at all," said Edmonton interim head coach Jay Woodcroft, who replaced the fired Dave Tippett in February. "What I've learned is he is a hockey player with really, really good habits.

"There's a reason why he finds success."

Markstrom, who allowed 11 combined goals in Games 1 and 2 after posting a .941 save percentage in the opening round against the Dallas Stars, got the hook in favour of Vladar to start the third with the Flames turning their attention to Game 4.

Seven points clear of Edmonton in the standings to top the Pacific Division and minus injured defenceman Chris Tanev (undisclosed) for a fourth straight contest, Calgary got a power play early in the final period looking for a spark, but Smith was sharp at every turn.

Lucic subsequently ran over the veteran netminder behind the Oilers' net midway through the third to ignite a melee involving all 10 skaters.

"When you're getting run through the end wall and you're not expecting it ... it's not an ideal situation," Smith said.

"A play out of frustration, running our goalie," added Kane.

Smith was removed by the spotter in favour of Koskinen, who didn't have to make a save in just over four minutes of action, before Edmonton's starter returned to a huge ovation after re-emerging from the locker room.

Kylington got a consolation goal for the visitors — his first of the playoffs — with under five minutes to go in regulation.

The Oilers fell behind early in both games at Calgary's Scotiabank Saddledome, but following a wild 9-6 loss in the opener, rebounded with a 5-3 comeback victory two nights later to even the series.

Edmonton had a much better start Sunday, including Brett Kulak's point shot that leaked through Markstrom and hit post before being cleared.

The Flames had hoped to keep the action at 5-on-5 as much as possible after McDavid, Draisaitl and the Oilers took advantage of power play, short-handed and four-on-four situations in Game 3, but took two penalties to Edmonton's one in the first.

McDavid, who seemed to have the puck all night, went on one of his jaw-dropping rushes during his team's second man advantage, but Markstrom was there to deny the Oilers captain in what was a sign of things to come.

"Good to come back home and play these guys on our home ice," Kane said. "A good win for our group."

And one he probably didn't envision being part of not that long ago.