Betsy tucked away chances in either half to give Brian Talbot's side just the lift they needed before the eagerly awaited live TV meeting. But Posh, also still in FA Cup contention, will have to make the trip to Nottingham Forest without influential former Welsh international Andy Legg.
After bringing Posh back into the game with his third goal of the season, 38 year-old midfielder Legg blotted his copy book when sent off for a 40th minute foul on Neil Kilkenny, a dismissal that will automatically rule him out of the City Ground tie.
Midfield veteran David Eyres, 41 next month, unsettled Post with an early inswinging free-kick and Oldham retained the initiative to go ahead on six minutes with Betsy finishing calmly as the home defence struggled to get the ball away after Mark Tyler parried Scott Vernon's stinging shot.
Posh hauled themselves level on 20 minutes, Calum Willock's accurate delivery finding Legg in the right place to fire left footed and low past towering goalkeeper Les Pogliacomi.
Forced to play 50 minutes with 10 men after Legg's red card, Posh chased the game but were caught sadly short of numbers at the back as Lee Croft set off on a 63rd minute break which ended with an inch perfect final pass to the ever alert Betsy who only had to tap it over the line.
Australian striker Jamie McMaster, making a debut on loan from Leeds United, rattled an Oldham post and Posh skipper Mark Arber, facing his former club, also went close with a blistering late shot.
Vernon, the man who dumped Manchester City out of the FA Cup earlier in the month, showed plenty of appetite for goalmouth action but failed to beat Tyler in the dying minutes.