Leicester moved seven points clear at the top of the Premier League with six games remaining after Wes Morgan’s header saw off Southampton 1-0.
The Foxes skipper connected with Christian Fuchs’ first-half cross to score his first goal of the season.
Southampton came closest when Sadio Mane rounded Kasper Schmeichel, but his goalbound shot was superbly blocked by Danny Simpson.
Leicester will win the title if they win four of their remaining games.
Claudio Ranieri’s side have now won five of their last six matches by a 1-0 scoreline, and after main title rivals Tottenham slipped up with a draw at Liverpool on Saturday, the most unlikely title triumph in Premier League history must surely be considered a probability now.
Southampton remain seventh after a first defeat in four matches.
Anthony Martial’s winning goal kept Manchester United in the chase for a Champions League place on the day they named a stand after Sir Bobby Charlton.
Martial turned in Tim Fosu-Mensah’s cross from close range early in the second half to send Everton to a third straight Premier League defeat courtesy of a 1-0 triumph.
Phil Jagielka headed against the bar for the visitors, and later had a snapshot saved by David De Gea.
Victory leaves United one point behind fourth-placed Manchester City.