Novak cut it to 2-1 at 19:15 with a backhand off a rebound from Mantha, but Matt Savoie extended it to 3-1 at 4:35 of the second period on a wrist shot through Skinner’s five-hole.
Karlsson pulled Pittsburgh to within 3-2 at 6:24, scoring with a one-timer set up by Crosby on a power play.
Bouchard made it 4-2 with a wrist shot at 9:36 for the Oilers’ third power-play goal.
“It was an exciting game, especially early,” Edmonton coach Kris Knoblauch said. “It was back and forth. Then it ended up being more of a special teams game. Fortunately, we were able to capitalize on three of them."
Vasily Podkolzin pushed it to 5-2 at 6:47 of the third period, scoring on a loose puck in the slot before Bryan Rust cut it to 5-3 at 16:51 by chipping in a puck from the crease.
McDavid scored into an empty net to make it 6-3 at 18:41, his 20th goal of the season.
Danton Heinen then finished a pass from Novak at 19:46 for the 6-4 final.
“The season's always going to be a bit of a roller coaster, and obviously right now we're in it in a downswing,” Rust said. “And I think we can't just go around here moping around and coming in every day with long faces. I think each day is a new day. Think about this one for the rest of the night, learn our lessons, move on.
“Obviously, we've had a few too many lessons to learn here recently, but we can't sit and sulk and dwell on it."
NOTES: McDavid and Draisaitl had at least four points in the same game for the 12th time, tying Ken Hodge and Phil Esposito for the fourth-most instances by a duo in NHL history, behind Wayne Gretzky and Jari Kurri (30 times), Bryan Trottier and Mike Bossy (23), and Bobby Orr and Esposito (13). Edmonton has never lost when they each record at least three points (47-0-0). ... Draisaitl is the fifth-fastest player born outside of North America to reach 1,000 points, behind Peter Stastny (682 games), Jari Kurri (716), Jaromir Jagr (763) and Nikita Kucherov (809). ... Penguins defenseman Brett Kulak, who was involved in the trade that swapped Skinner and Jarry, had two blocks in 15:22 of ice time in his Pittsburgh debut. ... Pittsburgh defenseman Jack St. Ivany had four hits and three blocks in 14:52 in his season debut after returning from a lower-body injury he sustained in a preseason game Oct. 1.