Ince had barely settled into his seat in the stands when his new charges took the lead, Ben Davies' corner headed home with purpose by Mike Edwards.
Ricky Ravenhill then saw his volley saved by Kelvin Davis, before a stinging free-kick from Rickie Lambert struck the post and Adam Lallana's long-range drive whistled over the crossbar for the Saints.
The tables turned in the 68th minute, though, as skipper John Thompson was controversially sent off for bringing down Lee Barnard in the area.
Lambert took the penalty and silenced the jeering Magpies fans by slotting low to Rob Burch's right.
Ince's debut went from bad to worse five minutes later as Barnard stabbed home from Lallana's corner, before Lallana turned scorer to complete the turnaround, sending a dipping shot into the far corner with the last kick of the game.