Wes Thomas opened the scoring for the visitors before Ince, who provided the cross for the first goal, made it 2-0 from the spot.
Dwight Gayle grabbed one back for Posh, but goals from Nouha Dicko and a second for Ince sealed the points for Blackpool late on.
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.
They continued to press as Tiago Gomes blasted a speculative effort from 30 yards that went just over the bar.
But Posh fired Appleton's side a warning shot shortly afterwards as George Boyd found himself clean through on goal and his left-footed strike forced Matt Gilks into a fine save with his feet.
Two minutes into the second half Blackpool's Chris Basham picked up a yellow card for a foul on Mark Little as Peterborough started well. It was his fifth booking of the season so he will miss the trip to Crystal Palace next week.
Before long the away side began to exert themselves on proceedings again, taking the lead in the 51st minute through Thomas.
Ince, a constant threat, played a delightful ball from the left-hand side which Thomas met perfectly to send it past Olejnik.
Appleton's side had their tails up 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 keeper the wrong way and score in the bottom-left corner.
Posh came back at Blackpool, throwing everything they had at them, and they were rewarded when 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 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 that sailed into the top-left corner.