However, a John Fleck effort in the 38th minute was punched away by the visiting keeper, dropping to Wilson and setting him up for a close-range finish.
Christie and Franck Moussa both tried to double the advantage before the break, but neither could find the target.
The hosts continued to dominate in the second half and extended their lead in the 59th minute, as Leon Clarke picked out Wilson, who was able to slot the ball past Walker from inside the box.
Moussa had two strikes on target in the next 15 minutes, but Walker was able to make a pair of solid saves.
The result leaves Coventry at the bottom of the table.