Late in the first period, Whitney got control of the puck at center ice, skated down the right side and eluded an Oilers defender before cutting to the net and slipping a shot under Devan Dubnyk for a 2-0 Coyotes lead.
Oliver Ekman-Larsson and Shane Doan also scored for Phoenix.
Mike Smith finished with 21 saves in the win, which sent Phoenix (73 points) past idle San Jose atop the division standings.
The red-hot Coyotes notched their fifth straight win and 10th in 11 contests.
Ryan Nugent-Hopkins returned to Edmonton's lineup following a 2 1/2-week absence with a sprained shoulder and celebrated by tallying the Oilers' lone goal.
Dubnyk allowed three goals on 20 shots in defeat.