With first-team coach John Schofield in temporary charge following the departure of Jimmy Mullen, Walsall started brightly pushing the ball around, but found themselves trailing following a defensive disaster.
Manny Smith failed to meet the ball when Charlie Lee whipped in a long throw and Craig Mackail-Smith flicked on for Whelpdale to poke in a low right-footed shot from 10 yards.
Walsall's defensive worries increased when defender Chris Palmer was stretchered off with a leg injury and 36-year-old Ince quickly became the busiest man on the park.
He dived right to block Aaron McLean's shot on the turn before denying George Boyd with a one-handed stop.
The Trinidad & Tobago international also did well to advance and take a Boyd cross as one-time Saddlers favourite Dean
Keates stormed in.
It was 35 minutes before Walsall managed a shot and even then Mark Bradley's effort was straight at Joe Lewis.
The Posh keeper was less certain just before the break but, despite missing the ball under pressure from hard working Jabo
Ibehre, he did get back to pluck a Troy Deeney lob from beneath the bar.
Ince was soon in second half action deflecting a Boyd shot against the foot of a post and then left his line to deny Mackail-Smith after the 18-goal Posh top scorer raced away from Tony Gerrard.
Curiously, Bradley could have levelled things on 78 minutes with a low cross-shot that flashed fractionally wide of Lewis' right hand post.
The action soon switched back to the other end and Ince performed another minor miracle to deny Mackail-Smith.