The two sides last played each other in a competitive fixture over 10 years ago when Rovers won an old Division Two fixture 3-1 in April 2003.
Tranmere won 2-1 at Chesterfield in the corresponding Capital One Cup tie last season before losing 3-0 at Aston Villa in Round 2.
Blue Square Bet Premier Division champions Mansfield, relegated from the Football League in 2008, won promotion back for the first time last season.
All ties are to be played during the week commencing August 5.
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