The visitors led when Koren netted on two minutes, beating David Marshall to the rebound after the keeper had parried Kevin Phillips’ shot.
Jamie Cureton then had two goalbound efforts blocked by Carl Hoefkens in quick succession midway through the first half.
Gera doubled Albion’s advantage on 71 minutes.
Jason Shackell’s header dropped to the Hungarian on the edge of the area and Gera took one touch before volleying into the bottom corner.
Norwich were handed a lifeline when Dion Dublin’s header struck Leon Barnett’s hand and Ched Evans kept his cool to stroke the ball into the bottom corner on 73 minutes.
City pressed for the equaliser but Albion weathered the storm to win.