Van Wolfswinkel was named in Chris Hughton's starting XI and he went close early on, whistling a shot narrowly wide from outside the box.
But Jonny Howson went one better after half an hour, getting in front of his defender and flicking in Nathan Redmond's cross from eight yards out.
Brighton should have equalised before half-time but Andrea Orlandi somehow missed the ball with the goal at his mercy and then fell over as he attempted to get a second bite.
Hooper came on for Norwich in the second half, but it was fellow summer signing van Wolfswinkel who had another chance, only to be denied by a good low save from Tomasz Kuszczak.
Brighton equalised with a stunning goal from Solly March, who unleashed a left-foot screamer from 25 yards out into the top corner of the net.
Norwich had a late chance to win it but Luciano Becchio headed back across the goal and wide of the target in front of an impressive crowd of 10,622.