Daniel Nardiello bagged his second goal in stoppage time to edge out the Latics in a thrilling League One encounter.
Man of the match Nardiello earlier broke the deadlock with a goal from the penalty spot after 21 minutes and things looked bleak for the visitors when David Mellor received a straight red card for a kick at Lee Frecklington five minutes before the break.
But two minutes later the visitors equalised following a great solo run by Cristian Montano and they took the lead after 52 minutes with a Matteo Lanzoni tap in.
However, Frecklington's glancing header from Ben Pringle's corner after 62 minutes levelled things up and Nardiello sealed it with a late winner after Mark Oxley saved Alex Revell's first shot but only palmed the ball straight to the Rotherham marksman.
"You couldn't tell we only had 10 men out there for more than half the game," said Johnson.
"The boys were fantastic. We have to keep going now for Crewe next week, but I honestly believe we can dig ourselves out of it.
"We scored a couple of goals away from home again today, though in the first 20 minutes we were poor and we were dictated to and played into their hands.
"Then three or four things didn't go right for us on the day when on another day the momentum would have swung our way."
Johnson said he didn't see the incident that led to Mellor being sent off, but said it was probably due to frustration because things hadn't gone right for the team.
"But if he kicked out, he will be disciplined and fined the maximum," said Johnson.