The hosts were first to threaten when Mark Irvine was brought down in the box but Marcus Barnes fired the penalty kick over the bar.
Layton Ndukwu put Jon Rudkin’s side into the lead just before the break, having netted for England’s Under-17s last month in a 2-1 defeat to Italy in the FA International Tournament.
And the young Foxes doubled their lead 20 minutes from time through forward Chris Dusabe.
The Saints snatched a goal late on through Barnes after the forward slotted in from close range, but the Hampshire club couldn’t find an equaliser.
Rudkin’s men have now totalled a good return of four points from three Premier League games.
They will host Tottenham Hotspur on Saturday at Belvoir Drive (KO 12pm).