But it was hard work for them as Hartlepool battled all the way and hit the woodwork three times.
Posh started well and home keeper Arran Lee-Barrett saved long-range shots from Charlie Lee and George Boyd before they took the lead in the 11th minute.
Sam Collins fouled Aaron Mclean a yard outside the area and Dean Keates curled his left-footed free-kick round the wall and into the top corner.
Hartlepool battled back and after Keates cleared a Michael Nelson header off the line, David Foley smacked a header against the visitors' bar. But it was a soft goal that earned the equaliser when 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.
Peterborough were back in front three minutes into the second half, Boyd slotting in from a few yards after Chris Whelpdale's shot was deflected into his path by Nelson.