But it was hard work for them as Hartlepool battled all the way and hit the woodwork three times.
Posh started like a train and home keeper Arran Lee-Barrett saved long-range shots from Charlie Lee and George Boyd before they took the lead on 11 minutes.
Sam Collins fouled Aaron McLean a yard outside the home area and Dean Keates curled his left-foot free-kick round the wall and into the top corner for a picture goal.
But Hartlepool battled back and, after Keates had cleared Michael Nelson's header off the line, David Foley smacked a header against the visitors bar.
But it was a soft goal that earned the equaliser. Andy Monkhouse's low right-wing corner was left at the near post by Paul Coutts, and keeper Joe Lewis couldn't stop the ball crossing the line.
But Peterborough were back in front three minutes into the second half, George Boyd slotting in from a few yards out after Chris Whelpdale's shot had been deflected into his path by Nelson.
Monkhouse hit the top of the bar with another corner and sub Joel Porter blasted a late shot against the underside of the bar, but Hartlepool couldn't find a breakthrough.