First-half goals for James Ward-Prowse and Jay Rodriguez plus a late penalty by Dusan Tadic led the Saints to a comfortable win that came at the cost of an injury to key defender Virgil van Dyke, who hobbled off in the second half.
Ward-Prowse opened the scoring after 26 minutes following good approach play from Cedric Soares, before Rodriguez doubled the lead in the 39th after reacting quickest to a bouncing ball in the box to fire a left-foot shot past the keeper.
After the break, Wes Morgan was fortunate when his own goal was ruled out for offside but Leicester's captain then held back Shane Long for a penalty that Tadic thumped home as Southampton emphatically ended a run of four successive league defeats.
"I think (in) the last matches I changed (the team's) shape to try to help my players play better but maybe I made mistakes," he said.
"Against Chelsea (in a 3-0 home defeat) we played three at the back and today we wanted to play with a diamond. The players are used to 4-4-1-1 and know the positions but I made a mistake.
"I think it is much better (to) give them what they know well. We tried to change our shape at halftime, to make a goal and we would have a chance to change the match. They won. They played better and deserved to win.