Oldham were in the relegation zone when Johnson, at 31 years old the Football League's youngest manager, took over the Boundary Park hotseat from Paul Dickov.
But they have earned 14 points from his eight games in charge and grabbed their latest victory with a last-gasp goal from Jean Yves Mvoto.
It was a third straight win for the Latics after they beat Bury and a Yeovil team managed by Johnson's father, Gary.
And Johnson said: "It wasn't a vintage performance but the lads have put in a monumental effort this week. I knew they would be leggy but we stuck to the gameplan and were defensively sound.
"I'm pleased with the run we've had since I came here and it's fantastic to be safe.
"It's a funny feeling because I'm a bit disappointed with our performance, but I'm delighted for everyone at the club and thankful that I've been given this opportunity.
"I've always believed in the players, but obviously there was a doubt over whether we would stay up. This has been an intense and mentally tough time for the players but hopefully they can enjoy our last two games.
"Now we need to end on a high and carry that form into next season. Hopefully, with the addition of players in key positions, we can start punching above our weight."