The Latics squandered a gift-wrapped opportunity to snatch a deserved draw when staging a rousing late fightback.
They trailed by two goals entering stoppage time but substitute Charlie MacDonald nodded his first for the club from point-blank range after being picked out by a terrific Connor Brown cross to raise hopes of an unlikely point.
And that is exactly what they should have earned as defender James Tarkowski contrived to miss an open goal with the last kick of the game after a James Dayton corner had been headed towards the target by debutant Joseph Mills.
But despite mis-firing for much of the match, it was Darren Ferguson's men who pocketed the points to extend one of only two remaining unblemished records at this level.
Record signing Britt Assombalonga had earlier delivered a stellar display to put Posh on course for victory. The 20 year-old hot-shot broke the deadlock with a scorching 25-yard strike 11 minutes before the break.
Assombalonga went from scorer to creator when being scythed down by Latics goalkeeper Mark Oxley to earn a late penalty.
Lee Tomlin, who saw a written transfer request snubbed by the club during the week, made no mistake from the spot moments after he had screwed another excellent chance inches wide.
But Posh so nearly threw it away in the dying moments as Oldham were left thinking about what might have been.
Boss Johnson said: "We showed again that we are not frightened of teams in this league.
"We kept going to the very end, got a good goal back and how James missed at the end I will never know.
"We probably did enough to deserve a draw and on another day could have won the game.
"Aside from conceding a couple of poor goals it was a really pleasing performance.
"There is a right way and a wrong way to lose games of football - and this was the right way."
Opposite number Ferguson was the first to admit his high-flyers were fortunate winners.
Posh have reeled off four successive victories in all competitions despite not hitting top gear.
Ferguson said: "We have to count ourselves lucky to win that game.
"We had so many players who were miles below par and yet we still managed to come out on top.
"I'm delighted to be winning games as that is what this business is all about, but there is a lot of stuff that I am not happy with.
"We have not been anywhere near our best so far this season and we need to work out why that is the case."