United ran out 2-1 winners at the Keepmoat Stadium at the same second round stage a season before last.
Leeds have won the last four meetings between the sides.
The last time these two sides met, in February 2012 at Elland Road, police had to prevent a tunnel bust-up escalating out of control following Leeds’ 3-2 victory - but the fracas still landed both clubs in hot water with the Football Association.
The tie will be played during the week commencing August 26.
Leeds made it through courtesy of a 2-1 win over League Two side Chesterfield at Elland Road, while Rovers won 1-0 at home to Rochdale.
Capital Cup 2nd round draw in full:
Stoke vs Walsall
Huddersfield vs Charlton
Aston Villa vs Rotherham
Tranmere vs Bolton
Morecambe vs Newcastle
Burnley vs Preston
Liverpool vs Notts County
Norwich vs Bury
Leyton Orient vs Hull City
Everton vs Stevenage
West Brom vs Newport County
Bristol City vs Crystal Palace
Peterborough vs Reading
Barnsley vs Southampton
Burton vs Fulham
Carlisle vs Leicester
Doncaster vs Leeds
Nottingham Forest vs Millwall
Sunderland vs MK Dons