Rovers were comfortably the more dangerous of the two side's and England Under-21 keeper made a hat-trick of great stops to ensure the names of both sides go into the draw for the third round.
Lewis kept out Ian Moore and Gareth Edds in the opening 15 minutes and he again spared the home side's blushes seven minutes from time with a point-blank stop to deny substitute Terry Gornell.
Posh will have to perform much better in the replay on Tuesday week to stand any chance of success as striker Aaron Mclean managed their only effort on target with a bouncing 25-yard drive midway through the opening period.
Posh were boosted by the introduction of substitute Shaun Batt at the interval, but the former Fisher Athletic man could not find a finish to complement some dangerous approach play.
Dean Keates and George Boyd also blazed wide as the clash ended in stalemate.