Leicester were being pinned back but did retain a counter-attacking threat whenever they broke past Southampton’s midfield press, particularly through Maddison and Ademola Lookman, who surged behind left-back Kyle Walker-Peters to force a corner.
The resulting cross was only partially cleared, with Maddison and Lookman then combining to tee up Wilfred Ndidi whose shot was saved by Alex McCarthy but directed back into the path of Jonny Evans to side-foot Leicester level.
Parity would last only 12 minutes, with Leicester only half-clearing another well worked Southampton corner to allow space for Nathan Redmond’s precise lofted cross between Castagne and Caglar Soyuncu, for Che Adams to deftly head past Schmeichel.
Worrying half-time scenes followed, with medics urgently entering a side stand to treat a fan who, it later emerged, had suffered a fit rather than a cardiac arrest. An announcement followed that the second half would be delayed by five minutes, and then another five minutes, before the fan was moved from the stand to applause from all sides of the stadium.
The players were then permitted an additional five minutes to warm-up, with Leicester clearly now refocused. Maddison was especially, drifting more dangerously into space in support of Vardy and, having been fed by Luke Thomas, produced a wonderful piece of individual skill. Running directly up against Tino Livramento, arguably Southampton’s player of the season, Maddison first cut back inside and then drilled a powerful shot beyond McCarthy.
The game seemed finally to be at Leicester’s mercy but they missed two excellent chances to clinch victory. First Ayoze Perez passed for Harvey Barnes, whose shot was brilliantly tipped wide by McCarthy’s outstretched hand.
A defensive mix-up between Walker-Peters and Salisu was then seized upon by Vardy but, having opened up his body for what looked like the winning goal, he lofted his side-footed shot over the cross-bar.