The Dutchman, who beat Chelsea keeper Petr Cech's 2004-05 Premier League record last week, moved past the all-league best of 18 hours, 23 minutes set by former Reading keeper Steve Death over two seasons during 1978 and 1979.
Van der Sar set the record when he kept Everton at bay for 72 minutes of Saturday's clash.
The last goal the Dutchman conceded was to Arsenal's Samir Nasri in a 2-1 away defeat in the Premier League on November 8. Saturday's game was his 12th successive league clean sheet since then with another in the FA Cup for good measure.
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