After second placed Tottenham slipped up at Liverpool yesterday, the Foxes came into the game knowing that a win will further put them away from their title rivals.
A Wes Morgan’s 38th minute header was enough for the Premier League leaders, as Claudio Ranieri’s side have now won five of their last six matches by a 1-0 scoreline.
The skipper connected Christian Fuchs’ cross to head home his first goal of the season.
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The visitors came close through Saido Mane, whose goal bound effort was saved brilliantly by Danny Simpson.
With six games left this season, Leicester will win their first ever Premier league title if they win four of their remaining games.
Speaking after the game, match-winner Wes Morgan said: “We saw the Tottenham game yesterday [Saturday] was a draw and wanted to make the most of our opportunity. We really wanted it today.
“I’ve been getting a lot of stick because I haven’t scored all season so it’s great to shut them up.”
Ranieri’s men travel to Sunderland on Sunday March 10.
Meanwhile, Southampton remain in seventh place after losing their first game in four matches.