An abject display from the Railwaymen had left Johnson's far from impressive outfit cruising to a vital victory thanks to Gary Harkins' goal, until the fourth official's board showing seven added minutes inspired a last stand from the hosts.
Chuks Aneke, a passenger for most of the afternoon, curled an exquisite free-kick towards goal which Paul Rachubka did well to claw over his crossbar.
But the Oldham goalkeeper was beaten straight from the resulting corner when Harry Davis planted his head onto George Evans' cross with 94 minutes on the clock.
It was a barely deserved leveller and one which visiting boss Johnson felt was a direct result of the "ridiculous" amount of time added on by referee David Phillips
He said: "It was a ridiculous call to have seven minutes of injury time.
"That enabled Crewe to launch the ball and they ended up getting a corner which they scored from. But I don't know where those seven minutes came from.
"We had frustrated them and we took over the game. We had four or five chances which could have finished them off.
"We are disappointed as the lads were strong and powerful on the break. We deserved to win the game."