The series is tied at one game apiece with the scene shifting to Edmonton for Game 3, which is Sunday night.
"It's playoff hockey. It's not going to be perfect every night", said Calgary forward Tyler Toffoli. "Things happen within a game. We have to stay composed and not take penalties and honestly, play our type of hockey."
"We battled harder, that was all", said McDavid. "It's just working, being harder in battles, winning some 50-50 pucks. We didn't win many in Game 1.
"Obviously., we defended better, I thought, still gave up some chances, but 'Smitty' played well."
Toffoli scored, and Jacob Markstrom made 35 saves for the Flames.
"I think we got away from our game and started playing their type of game, and when that happens, they have guys who can do the types of things that they did, and we didn't do a good job", Toffoli said.
Story of the game
Michael Stone put Calgary in front just 3:02 into the game, scoring on a slap shot from the point after his initial one-timer was blocked by Jesse Puljujarvi.
It was 2-0 after Brett Ritchie fired in the rebound of a point shot by Erik Gudbranson.
"We didn't get the start we wanted, didn't make it easy on ourselves", McDavid said. "But obviously responded well."
Keith cut the lead in half as McDavid fed him a one-handed pass and he scored on a one-timer from the left circle. At 38 years and 308 days old, he became the oldest player in Edmonton history to score a playoff goal.
A little more than two minutes into the second period, Toffoli restored the Flames' two-goal lead, one-timing a pass from Elias Lindholm from below the left circle on the power play.
Draisaitl appeared to score 29 seconds later on the rebound of an individual move by McDavid, but Calgary coach Darryl Sutter challenged the play for goaltender interference, and the call was reversed after a video review.
McDavid brought the Oilers to within 3-2 after taking a return pass from Keith and deking Markstrom before tucking the puck past his right pad.
McDavid is the first player to get at least 20 points (six goals, 14 assists) in the first nine games of a postseason since Mario Lemeiux (nine goals, 13 assists) did so for Pittsburgh in 1992.
"He's the best player in the world and he's pushing himself", Hyman said. "When you're the best, it's easy to be comfortable because guys are chasing you, but it's hard to keep pushing and challenging yourself, and he's a guy who wants to win more than anybody."
Evan Bouchard tied the game with a slap shot past the blocker of Markstrom on the power play.
"We're kind of leaving our foundation a bit and playing into their hands", Flames defenseman Noah Hanifin said. "When you're playing those four-on-fours and you're short a lot, it's tough.
"We've got to clean that up for sure. 'Marky' made some huge saves for us and kept us in it."
Edmonton took the lead for the first time in the game a little more than halfway through the third period as Hyman beat Markstrom high to his glove side.
Draisaitl then shot low blocker side on his own breakaway at 2:32 later for the 5-3 final.
"I think it's an emotional roller-coaster", Hyman said. "You've got to try to stay off of it as much as you can and stay even-keeled because it's hockey, and some nights bounces are going to go your way and some nights they aren't.
"We've had kind of a roller-coaster season where our backs have been against the wall, and our ability to push back has been second to none to any team i've been on."