Toews had a hat trick as the Blackhawks blanked the Oilers 5-0 on Wednesday night.
Chicago goalie Marty Turco earned the shutout, having to stop only 18 shots.
It was only the second career regular-season hat trick for Toews, who notched his first in February 2009 against Pittsburgh and then again in the playoffs against Vancouver.
"It's fun when they all go in, especially early in a game like that," he said. "Hopefully I can keep it rolling. I just need to stay confident around the net and know that if I keep shooting, it is going to go in."
Toews said his team wanted to have a stronger showing against the Oilers, who have had half of their four wins come against the Hawks in two road victories this season.
"For sure there was a bit of a revenge factor," he said. "We mostly felt we had ourselves to blame in the first couple games. It's always been about how we play and prepare and the two games we played against them we weren't good enough. We definitely wanted to come back with a good one tonight."
The Oilers (4-10-3) have lost five games in a row and have only two wins in their past 15 outings, both against Chicago. Edmonton has been outscored 30-8 in its past five games.
Oilers head coach Tom Renney said that while the team is in definite rebuilding mode, the effort still has to be there.
"We have a ways to go, there's no doubt about it," he said. "We all want this to happen real quick. We all want it to have happened tonight and last week and a month ago. We'd be kidding ourselves if we thought that was going to be the case. But we need to be more competitive. This needs to mean more to us than what we have demonstrated in the last little while.
"It looked like we had some passengers."
Chicago started the scoring with five and a half minutes to go in the first period. Brent Seabrook's shot was stopped by Edmonton goalie Nikolai Khabibulin, but Toews was on the doorstep to dig the puck out of his equipment and into the net.
Toews got his second of the night on the power play with 46 seconds left in the opening frame, as he banked a shot off the skate of Oiler defender Tom Gilbert to make it 2-0.
The Hawks badly outshot Edmonton 20-4 in the first period.
While shorthanded and with just over a minute left in the second Jake Dowell's breakaway shot rang off the post only to see Kurtis Foster cough it up seconds later to Sharp, who deked Khabulin for his 11th of the season.
Chicago finished the rout two minutes into the third as Bickell unleashed a cannon past Edmonton goalie Devan Dubnyk, who replaced Khabibulin to start the third.
Chicago outshot Edmonton 47-18 in the contest.
Turco was most impressed with his team's defensive play on the night.
"It was a huge team win," he said. "Five goals is great but I think it was signified better by the zero on the other side of the board."
Both teams are back on the ice on Friday as the Oilers play host to Phoenix and the Hawks travel to Calgary. ... It was the start of a six-game road trip for the Blackhawks as the circus does its annual stint in Chicago. ... Edmonton won the two previous meetings between the two teams defeating the Hawks 7-4 and 2-1, both games in Chicago. ... The Blackhawks won all four games against the Oilers last year. ...There was a brief video tribute honoring former Oiler turned Blackhawk forward Fernado Pisani. The Edmonton native was the Oilers' 2006 playoff hero with 14 goals in their run to the Stanley Cup finals and joined the Hawks as a free agent this summer. ... With Ladislav Smid out after being jumped by Sean Avery in a game against the Rangers on Sunday, the Oilers called up defenseman Shawn Belle for the game. Forward Jean-Francois Jacques also played his first game for the Oilers this season. ... Last year's Norris trophy winner Duncan Keith came into the game with a minus-six rating.