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After a fairly even start, it was the hosts who made the breakthrough at Carrow Road as Johnson found space inside the Tractor Boys' box and rifled the ball into the top corner to give his side the advantage.
Sears had a couple more first-half opportunities to equalise for the visitors, but was unable to finish his chances.
Substitute Cameron Jerome made an instant impact for the Canaries in the second half as his attempt on goal from the edge of the area was blocked and then deflected in by teammate Lewis Grabban to double Norwich's lead.
Ipswich failed to threaten the Norwich goal as they succumbed to a fourth straight defeat to their local rival and one which sees them slip to sixth in the standings.