The Wales international registered his first league goals since September to move Forest above their East Midlands rivals, who have now lost four in a row, and four points clear of the relegation zone.
It is a marked turnaround since the reverse fixture in October that saw Leicester win 4-0 which Forest boss Steve Cooper called the worst game of his managerial career.
His side looked doomed that night, but now they have real hope of staying out of relegation trouble after an impressive run that has seen them lose just one of their last six Premier League games.
That victory kick-started Leicester's season but their form has been woeful since the season resumed after the World Cup as they have lost all four games.
The pressure is back on Brendan Rodgers, who is desperate for reinforcements this month as his side try to avoid getting pulled back into a relegation scrap.
Forest were full of early bluster and Ryan Yates had two chances to break the deadlock but first he could not get enough on his header from Remo Freuler's cross and then he shot wide when things opened up for him 20 yards out.
But the best opening came Leicester's way in the 14th minute and Harvey Barnes should have buried it.
Marc Albrighton forged down the right and sent an inviting cross which fell perfectly for Barnes, but the forward put his first-time shot wide.
Forest continued to be brighter but they could not test Danny Ward as the first half ended goalless.
Barnes was guilty of another poor miss early in the second half as he put his shot wide from a golden position after Youri Tielemans had robbed Freuler.
That wasted chance proved costly as Forest took the lead in the 56th minute.
A quick break saw Morgan Gibbs-White send Johnson clear and the Welshman rounded his international team-mate Ward and rolled into an empty net.
The linesman's flag went up for offside but VAR overturned the decision and Johnson's first Premier League goal since September stood.
It was Forest who pushed for a second and it should have come in the 72nd minute as Sam Surridge was presented with a perfect opportunity from Serge Aurier's cross but he flashed his free header from eight yards wide.
That miss did not prove too costly as Forest made the game safe in the 84th minute as Johnson bagged his second.
Gibbs-White carried the ball forward and played the perfect pass for his team-mate to coolly slot home and ensure the three points were staying at the City Ground.