With 87 minutes on the clock and the game locked at 1-1 Johnson, who scored a cracker in Saturday’s 3-0 win over Watford, curled a glorious left foot shot over Paul Robinson to put the Canaries ahead.
Lewis Grabban then scored his second of the night deep into injury-time to confirm City’s second win of the season.
Rovers made a sensational start, taking the lead from their first attack of the game after just 43 seconds.
A deep free-kick from Marcus Olsson, whose twin brother Martin was suspended for Norwich, picked out Rudy Gestede and the striker’s nod on found Tom Cairney who converted brilliantly with his left foot from all of 25 yards.
The visitors had caught Norwich completely cold and had decent claims for a penalty turned down a couple of minutes later when the ball appeared to strike Steven Whittaker on the arm in the box.
The Canaries finally awoke from their slumbers though, with Alex Tettey striking the outside of the upright after being fed by Wes Hoolahan and Kyle Lafferty testing Paul Robinson from distance.
It was all Norwich now and they got back on level terms on 23 minutes when Hoolahan’s cross was blocked by the arm of Jason Lowe and referee Graham Scott pointed to the spot.
Robinson saved Grabban’s penalty but the rebound fell kindly for the summer signing to net his second goal in as many games.
City continued to have the better of it as the half progressed and it required a perfectly timed tackle from Grant Hanley to deny Grabban a chance for his second just before the break.
The pace of the game dropped during the early stages of the second period although Robinson had to be alert to Nathan Redmond from close range as the game approached the hour mark.
The Canaries went even closer to an equaliser eight minutes later, with half-time substitute Ryan Bennett seeing his header from a Tettey cross clip the crossbar.
It was all Norwich now and it looked for all the world that they would move ahead when Grabban connected perfectly with Redmond’s cross from the right on 70 minutes.
But Robinson somehow kept out the striker’s close range header, touching it onto the bar before the ball was hacked clear.
Blackburn were defending well but posed no real threat at the other end, and it was the hosts who continued to dominate, and they finally got their reward when Johnson beat Robinson from long range.
There was still time for Rovers to come close to an equaliser following a goalmouth scramble but Norwich had the final say on the breakaway, with Robinson up for a corner and Grabban firing home at the second attempt.