EDMONTON -- Going on their longest road trip of the year hasn't slowed the Chicago Blackhawks down one bit.
After starting the trip with a disappointing 5-1 loss in Colorado, Shaw said the Hawks have regained their form.
"We've got back to our systems and rolling all four lines," he said. "Everybody is bringing the energy we need them to and the chemistry through all four lines is pretty amazing right now. We've been playing some of our best hockey.
"We've had a couple of injuries to key people, but everybody is stepping up. That's why our game has improved."
The Blackhawks moved ahead of Anaheim and into first place in the NHL with the victory.
Chicago goalie Corey Crawford made 24 saves to collect his 16th win of the season.
"We are just taking it game by game and trying not to look too far ahead," he said. "We are a very focused team right now. Playing in a building where we haven't had much success of late, it was nice to come in here and get off on the right foot and get a couple of goals early."
In the 2011-12 season, the Blackhawks lost 9-2 and 8-4 in Edmonton.
Chicago head coach Joel Quenneville said the key was getting two early goals and putting the Oilers on their heels.
"We had a great start in the game," said Quenneville. "We get that short-handed goal and we have a red-hot power play that got us off on the right foot. Getting off to that start was important. The special teams in the first period really put us in a good spot. Across the board, we did what we were looking to do and played a really solid game.
Justin Schultz replied for the Oilers (7-16-2), who saw a season-high three-game winning streak come to an end.
"It was a crazy game to me a little bit," said Oilers head coach Dallas Eakins. "It wasn't a 5-1 game, I thought it was probably a 3-1 game. But giving up that shorty early, where we bobbled the puck, cost us. Then we couldn't kill that penalty and when you're down 2-0 to the defending Stanley Cup champions, it's usually going to be trouble right away."
Oilers forward David Perron said his team just seemed flat.
"They pretty much beat us in every aspect tonight," he said. "I felt like the energy was pretty low for having three days off. It's a disappointing game for us wanting to make a statement.
"We have to find an answer in here. I feel like we should have had better energy after three days off like that."
Chicago got on the board five minutes into the first period with a short-handed goal as the Oilers Nail Yakupov couldn't corral a bouncing puck at the blue-line, allowing Toews to take off on a breakaway. The Blackhawks captain waited for Edmonton starter Devan Dubnyk to commit before scoring his 12th goal of the season.
Chicago made it 2-0 three minutes later on the power play as Edmonton's defenders failed to clear a puck in the crease, allowing Kane to swoop in and score into a wide-open net with Dubnyk down and out of the play.
The goal extended Kane's league-high point scoring streak to 11 games. He has six goals and nine assists during that span.
The Oilers best chance came with four minutes left in the first period as Ryan Smyth got off a point-blank shot from the side of the net, but Crawford came across for a big pad save.
Chicago went up by three goals a minute-and-a-half into the second period as an Oduya shot bounced off the glove of Edmonton defenceman Corey Potter and into his own net.
The rout was on as the Blackhawks made it 4-0 six minutes into the middle period on a three-on-one as Jeremy Morin made a backhand pass to Shaw who had a ton of net to deposit the puck into.
That goal spelled the end of the night for Dubnyk and set the stage for the debut of Ilya Bryzgalov.
The veteran goalie, who signed a free agent deal with Edmonton on Nov. 8, hadn't played an NHL game since becoming a compliance buyout of the Philadelphia Flyers in June with seven years remaining on his nine-year, US$51 million contract.
The move seemed to spark the Oilers, as they finally got a goal past Crawford eight minutes into the second as Schultz snuck in from the point and unleashed a bullet from near the face-off dot to make it 4-1.
Shaw hoped he had his second of the night on a late third period power play, but the goal was immediately waved off as he had clearly kicked it into the net.
With two minutes remaining, however, Shaw did get another goal as he tipped a Nick Leddy shot past Bryzgalov for his seventh of the season.
Bryzgalov made 12 saves on 13 shots in his return to an NHL net.
The Blackhawks play the fifth game of their seven-game road trip in Calgary on Wednesday, their annual trip that coincides with the circus hitting Chicago. The Oilers start a three-game road trip in Nashville on Thursday.
Notes: It was the second of three meetings between the two teams this season. The Blackhawks won the first match-up 5-4 in Chicago on Nov. 10 on the strength of a three-goal third perioda Oilers goalie Devan Dubnyk was named the NHL's third star of the week on Monday after only allowing one goal in a pair of wins over Columbus and Floridaa Chicago winger Marian Hossa missed the game to attend to a family matter, while fellow forward Bryan Bickell missed his third straight game with a lower-body injury. There was some good news for the Hawks, however, as centre Michal Handzus played his first game since Oct. 24, returning from a hand injurya The oft-injured Oilers are actually remarkable healthy at the moment, with non-starting forwards Tyler Pitlick and Ryan Hamilton and third-string goalie Richard Bachman on the shelf.