The league leaders were behind to Scott Vernon's goal on the stroke of half-time when Johnson was introduced as a with little over 20 minutes remaining.
Within 10 minutes the former Stockport striker had prodded home an equaliser. Then, deep into injury-time he headed home a corner from Anthony McNamee.
Southend had been under pressure from the very first minute when Stephen Hughes fired wide from a good position, but they defended bravely and stunned Norwich seconds before the break when Vernon fired home from close range after Damien Scannell's cross had rebounded off Gary Doherty.
The second half saw Norwich lay siege the Southend goal without looking particularly convincing, and it took Johnson's intervention to change the course of the game.
In the 77th minute he was ideally placed to convert after Grant Holt's shot was brilliantly saved by Steve Mildenhall and then, from virtually the last kick of the game, he rose majestically at the near post to steal all three points.