The Posh striker's timing was perfect, scoring a goal at the end of each half. In between Adam Newton struck for the visitors to leave Bury in relegation trouble.
Just when they thought they were pulling clear of trouble with two wins and two draws from their last four games this defeat pushes Bury right back into hot water.
But victory for Peterborough ended their own run of four outings without a win.
Bury enjoyed at least an equal share of chances and possession in the opening half and for the first 15 minutes after the restart they were the brighter side.
But just when it looked as though their hard work would pay off Crow punished them in the 48th minute.
Newton doubled Posh's advantage on 62 minutes before ref Mike Pike gave Bury a lifeline, awarding a penalty against Mark Arber for a foul on Lewis Gobern.
Tom Kennedy converted the spot kick but despite Bury pressure Crow struck again in stoppage time to complete the visitors win and add to a 4-1 home win when the sides met earlier in the season.