Albion have been drawn at home to Championship rivals Reading in the third round of the FA Cup.
The tie will take place on the weekend of Saturday, January 4, which is two months before the Royals come south in the league.
Oscar Garcia's men drew 0-0 at the Madejski Stadium earlier this season.
The draw means Albion will have three home games in the first 11 days of 2014.
Crawley have been paired with Birmingham City, providing the Reds first negotiate their replay with Bristol Rovers.
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