The striker came on 14 minutes from time and the substitution proved to be a masterstroke from Addicks boss Phil Parkinson as Wagstaff rifled home a 25-yard strike to secure three precious points.
David Mooney put Charlton in front in the first half, but they were pegged back when Denis Behan scored from the penalty spot after Miguel Llera fouled Anthony Sweeney.
Striker Mooney headed beyond Scott Flinders after 31 minutes in a disappointing first half to put the Addicks on course to extend their unbeaten run to 11 matches in all competitions.
But Llera got the wrong side of Sweeney six minutes into the second half and when the Pools midfielder went down the referee pointed straight the spot, with Behan making no mistake from 12 yards out.
Charlton responded and Jonjo Shelvey hit the post, then Lloyd Sam and Mooney went close before Wagstaff produced a moment of magic to consign Pools to a fifth consecutive away defeat.