Richarlison got the 'Toffees' off to the perfect start as he opened the scoring after just seven minutes, but Ricardo Pereira's first goal for the 'Foxes' drew them back level just before half-time.
Wes Morgan's red card then made the visitors favourite to go on and find a winner and they did just that via's Sigurdsson stunning late goal.
Kurt Zouma confidently brought the ball out from the back and fed the playmaker, who looked to be under control as he received the ball facing his own goal.
However, nothing could have been further form the truth as he spun away form James Maddison with a glorious turn and took aim from fully 30 yards.
His strike was true and hard and flew past the reach of the diving Kasper Schmeichel before dipping wickedly to nestle in the top corner.
It was a goal worthy of winning any game as Marco Silva's side move into the Premier League's top half.