Despite starting the better of the two teams West Ham fell behind on 31 minutes to something of a worldy, as the Saints' Perraud fired home from some 27 yards leaving Alphonse Areola clutching at thin air.
West Ham lost key midfielder Tomas Soucek to a nasty facial injury five minutes into the second half after the Czach Republic international felt the full force of an elbow in the face by Southampton's Ibrahima Diallo,
While the VAR team who checked the incident - albeit briefly - felt there was no malice involved, TV replays suggested the French midfielder was perhaps somewhat fortunate to escape without a red card.
With Said Benrahma on for Soucek, who was given stiches upon leaving the field the Hammers were to strike next when Michail Antonio scored his first goal in claret and blue since New Years Day just ahead of the hour mark.
The number nine poked the ball over the line after Issa Diop had beaten the decidedly-dodgy Willy Caballero to Jarrod Bowen's near post corner, putting West Ham back on level terms.
Yet VAR - which was being employed due to the match being staged at a Premier League venue, unlike some other fifth round ties - was to come to Southampton's aid once again five minutes later when half time substitute Armando Broja was tripped inside the box by Craig Dawson.
That a foul by Broja on Dawson moments earlier was not checked was mystifying, however after three minutes' of deliberation and a pitchside check by referee Andre Marriner, Saints captain James Ward-Prowse stepped up to fire the hosts back into the lead.
Rather than responding positively at this point, with just a quarter of the match remaining, West Ham's tired troops spent much of the remainder on the backfoot and only Dawson's 89th minute header - which produced Caballero's only notable save of the night - threatened to send the game into extra time.
Yet in the fourth of seven added-on minutes Broja put the tie beyond any doubt when he weaved his way through a static West Ham defence before firing across Areola to give the home side a 3-1 win and passage though to the last eight of the competition.
For West Ham, now out of both domestic cups, the only chance of silverware remains the Europa League where they face crack Spanish outfit Sevilla. Before that particular encounter however comes a trip to Liverpool, where United have won just once since 1962...