Draisaitl made it 5-3 at 19:37, avoiding Pittsburgh defenseman Brian Dumoulin and scoring on the backhand.
"We just got on our heels, we didn't forecheck well and gave them some time and space," Crosby said. "They're a dangerous team and so, if you give them some time and space, they're going to make plays and we found that out."
Ryan McLeod scored off a drop pass from Derek Ryan at 16:45 of the third period for the 6-3 final.
"It's on the players. The players were the ones who decided to get it together a little bit," Edmonton coach Jay Woodcroft said. "There were some things in the first period that we wanted to clean up as a team, but it's the players who are the ones that go out and do that.
"Full marks to our players for playing probably our best period of the year in the second period, and that set us up for success tonight."
NOTES:Crosby extended his point streak to three games (two goals, three assists) and has 11 points (four goals, seven assists) in six games. He tied Adam Oates for 18th on the NHL's all-time points list with 1,420 points (521 goals, 899 assists). … The Oilers outshot the Penguins 26-4 in the second period, setting a franchise record for the most shots in a period. … Edmonton center Connor McDavid left at 3:31 of the second when he crashed into the goal post but returned later in the period. … Penguins forward Drake Caggiula had one shot on goal, one hit and one blocked shot in 7:28 of ice time in his season debut after being recalled from Scranton/Wilkes-Barre of the American Hockey League earlier Monday.