The home side were ahead 10 minutes before half time when McCormack stepped up and curled a 25-yard free kick around the wall and into the top corner of Westwood's goal.
Fulham doubled their lead seconds before the break when Hutchinson nodded home his first goal at Craven Cottage, from Bryan Ruiz's deep free kick.
McCormack went close with another set piece 10 minutes after the restart, before Stevie May and Christopher Maguire sent long-range efforts over the bar as the visitors searched for a way back into the game.
However, Wednesday's fightback was killed off when Fulham broke with lightning speed from a corner, with Christensen finishing off the move to atone for his earlier miss.
The result sees the Cottagers move up to 13th, with Sheffield Wednesday falling to 14th.