Southampton remained deep in relegation trouble after they were held to a 0-0 draw at a lacklustre Leicester City in the Premier League on Thursday.
Leicester, managed by former Southampton boss Claude Puel, now have gone five home matches without a win but the Saints produced little to scare them.
Jamie Vardy went closest for the Foxes, forcing a fine save out of Alex McCarthy in the second half and Riyad Mahrez shot just wide in the latter stages.
Southampton, in 18th place, are four points away from safety with four games remaining and face Chelsea on Sunday in the FA semi-finals.
At Burnley, Victor Moses struck a 69th-minute winner for Chelsea to give Antonio Conte's side a 2-1 victory over Burnley in the match played at Turf Moor.
Chelsea had taken a 20th-minute lead through a Kevin Long own goal and were well in control of the game before Burnley drew level when Johann Berg Gudmundsson's low drive went in off Burnley striker Ashley Barnes.
But the Blues restored their lead when a cross from the left from Emerson reached Moses at the back post and he took his time before firing past Nick Pope.
The win moved fifth-placed Chelsea to within five points of fourth-placed Tottenham Hotspur. The loss ended Burnley's five-match winning streak.