It was Turco's first shutout since coming to Chicago from Dallas this season. He had 40 shutouts during his nine years with the Stars.
Turco had to make just 18 saves to turn aside the Oilers, who have lost five in a row.
Toews scored twice in the first period, producing a power-play goal with 46 seconds left in the stanza. He completed his hat trick 1:12 into the second, after which Chicago got goals from Patrick Sharp and Bryan Bickell.
The first four goals came against Nikolai Khabibulin on 31 shots. He was relieved by Devan Dubnyk.
Edmonton had defeated Chicago in two previous meetings this season. Those victories represent half of the Edmonton win total for the campaign.