Fasth turned aside nine shots in the first period while the Ducks were grabbing a 2-0 lead on tallies from Ryan Getzlaff and Radek Dvorak.
The Swedish goalie went on to record his fourth whitewash of the season as Anaheim officially corralled its first division crown since 2006-07, when they won their only Stanley Cup championship.
Sami Vatanen added a third-period marker and Corey Perry helped out with two assists as the Ducks logged their 11th straight win in Edmonton and second in two nights.
Nikolai Khabibulin made 25 saves for the Oilers, who played without forward Ryan Nugent-Hopkins.
The first overall pick of the 2011 draft was out with a shoulder injury that will likely require surgery.