It was Leicester's first win in the league in six attempts and no-one had a brighter smile afterwards than Hume who lit up the game with two fantastic goals.
The opening exchanges had been fairly even until City broke the deadlock on 35 minutes with a cracking goal from livewire Hume.
There seemed little danger when the former Tranmere hitman received the ball well clear of the Southampton goal.
But a quick turn and drop of the shoulder took him clear of two defenders to create for himself the space to beat Kelvin Davis with a wonderfully struck shot from 25 yards.
And the Foxes were quick to scent a second goal with first Elvis Hammond sidefooting a Josh Low cross just wide and then Davis getting down well to keep out a Nils-Eric Johansson header.
But, as the interval approached, gaps suddenly began to appear in City's previously well-drilled rearguard with Bradley Wright-Phillips firing over from close range, before Saints levelled in time added on when John Viafara ran on to a splendid pass from Grzegorz Rasiak to guide the ball beyond the advancing Conrad Logan.
Southampton's fluent football continued after the break and they should have gone in front on 51 minutes when Wright-Phillips against found himself in the clear, but this time Logan sprinted off his line to dive bravely at the feet of the Saints striker.
But it was Leicester who regained the lead with another memorable strike by Hume on 62 minutes.
Claus Lundekvam and Hammond went up for a challenge and, when the loose ball fell to Hume, he hit a first-time volley to beat Davis from fully 25 yards.
It took just a minute for Southampton to level again, this time Inigo Idiakez drilling a low shot beyond Logan from well outside the penalty area.
But City conjured up a third goal in as many minutes when Johansson's shot struck the bar with substitute Richard Stearman reacting quickest to bundle the ball home from close range.
Both sides had chances to add to their goal tally, but it was Leicester who hung on for a win they just about deserved.