The Trinidad and Tobago international was beaten by Chris Whelpdale after just six minutes of Saturday's League One contest but then produced a catalogue of fine saves to make sure the Saddlers did not sink without trace.
Whelpdale was on hand to prod home from close range after Craig Mackail-Smith had flicked a long Charlie Lee throw into his path but proved to be the only player able to beat Ince.
The Walsall shot-stopper prevented Aaron Mclean and George Boyd doubling the home side's lead before the interval and he was in even better form after the break.
Ince deflected a Boyd drive against an upright moments after the restart before blocking from Mackail-Smith when the home striker was clean through on goal.
Walsall, under the control of caretaker boss John Schofield, were rarely seen as an attacking force. Mark Bradley fizzed a first-half volley straight at Posh goalkeeper Joe Lewis before screwing a second-half opportunity across the face of goal.