The Seasiders took the early initiative, with Craig Cathcart's header from six yards drawing the first save of the match from Robert Olejnik after a decent free-kick was whipped in from just outside the box by Ince.
Blackpool continued to press as Tiago Gomes blasted a speculative effort from 30 yards that went just over the crossbar.
In the 51st minute of the game, Ince, a constant threat, played a delightful ball from the left-hand side which Wes Thomas met perfectly to send past Olejnik.
Michael Appleton's side had their tails up by now and their second goal arrived from the spot after Thomas was brought down by Shaun Brisley in the 57th minute. Ince stepped up to send the goalkeeper the wrong way and score into the bottom corner.
Posh came back at Blackpool, throwing everything they had at them, and they were rewarded when Dwight Gayle pounced on a back-pass from Alex Baptiste to pull one back in the 70th minute.
But any hopes of a comeback were dashed 12 minutes later as Nouha Dicko slid in to connect with Angel Martinez's cross and make it 3-1.
Blackpool were not done as Ince capped off a fine individual performance with a superb strike from 20 yards which sailed into the top corner.