The tie against the League Two side will take place at Ewood Park during the week commencing Monday 22nd August.
Owen Coyle's side booked their place in the draw courtesy of a 3-1 win over Mansfield Town on Tuesday night.
Crewe progressed to the second round with a 2-1 win away to Sheffield United after extra-time. Ryan Lowe scored both goals for Steve Davis' side, who also kicked off their league campaign with a 2-1 away win.
The two teams have played against each other on just seven occasions in their history, with Rovers edging the head-to-head record by three wins to two.
The last meeting between the sides came during Rovers' promotion-winning season in December 2000, when a goal from Matt Jansen secured a 1-0 home win.
There has been just one previous meeting between the two clubs in the League Cup - in October 1998 - when Rovers again claimed a 1-0 win. Chris Sutton getting the goal on this occasion.
Second round draw in full:
Queens Park Rangers v Rochdale
Scunthorpe United v Cardiff City/Bristol City
Watford v Gillingham
Peterborough United v Swansea City
Everton v Yeovil Town
Millwall v Nottingham Forest
Sunderland v Shrewsbury Town
Luton Town v Leeds United
Chelsea v Bristol Rovers/Bristol City
Burton Albion v Liverpool
Rovers v Crewe Alexandra
Accrington Stanley v Burnley
Crystal Palace v Blackpool
Morecambe v Bournemouth
Preston North End v Oldham Athletic
Oxford United v Brighton and Hove Albion
Reading v MK Dons
Fulham v Middlesbrough
Newcastle United v Cheltenham Town
Exeter City v Hull City
Derby County v Carlisle United
Northampton Town v West Bromwich Albion
Wolverhampton Wanderers v Cambridge United
Stevenage v Stoke City
Norwich City v Coventry City