Southern blasted home from 12 yards following Stephen Crainey's cross while City's James Chambers lay injured.
The home side were upset that Blackpool played on but only had themselves to blame for a series of misses.
Iain Hume twice went close, Mark De Vries hit the bar and sent a header wide and sub DJ Campbell was denied by their impressive keeper Paul Rachubka.
Blackpool manager Simon Grayson on their controversial goal:
"Do you kick the ball out when you are in the opposition 18-yard box? It is a difficult one for the player on the ball because sometimes the injured player jumps straight back up as soon as the whistle goes.
"If we had kicked it out and Chambers had got back up it would have been a
wasted opportunity for us.
"Perhaps the referee should intervene in these situations and take the
decision out of the players' hands."
Leicester: Henderson, Chambers (Stearman 65), McAuley, N'Gotty, Mattock (Hayes 69), Newton, Kishishev (Campbell 55), Clemence, Wesolowski, Hume, De Vries.
Subs Not Used: Nielsen, Fryatt.
Blackpool: Rachubka, Barker, Jackson, Evatt, Crainey, Taylor-Fletcher (Jorgensen 69), Southern, Fox, Hoolahan (Hills 81), Parker, Morrell.
Subs Not Used: Vernon, Gorkss, Burgess.
Goals: Southern 63.
Ref: A D'Urso (Essex).