Leicester dominated the first half but could not break down a disciplined Watford defence until the 56th minute when Mahrez curled a sweet strike into the top corner of the net from the edge of the penalty area.
Mahrez continued to torment the Watford rearguard and Foxes defender Robert Huth missed a good chance to double the lead.
Leicester are five points ahead of Tottenham Hotspur, who drew 2-2 with Arsenal earlier on Saturday, and firmly on course for their first top-flight title with nine games remaining.
(Reporting by Ed Osmond; Editing by Ken Ferris)
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