Depending on results elsewhere, a win for the Norfolk side could see them leapfrog Watford to lead the Championship standings with five matches left to play.
It was hosting Norwich that dominated the opening exchanges as they forced a number of corners, but they were unable to make the most of any of those situations.
Then, within the space of two minutes, the visitors carved out two good opportunities.
Up the other end, the Canaries were finding clear openings hard to come by and were largely limited to efforts from distance, one of which saw full-back Steven Whittaker fire well over in the 26th minute.
However, that changed in the 33rd minute when Whittaker hoisted a high ball towards the back post. Johnson rose highest to meet it and his downward header got the better of Keiren Westwood, who could do little to prevent the ball entering his net via the post.
As the half drew to a close, Norwich continued to dominate proceedings and they were rewarded in first-half stoppage time when Johnson sent a half-volley beyond Westwood's reach to put his side in command.