Rovers have been drawn away to League Two side Newport County in the third round of the Emirates FA Cup.
The tie will take place at Rodney Parade over the weekend the 9th/10th January 2016 and will be the first ever meeting between the two teams.
John Sheridan's side required a replay to see off Brackley in the first round. Following a 2-2 draw away from home, Newport romped to a 4-1 win in the replay.
The South Wales outfit then won 1-0 away at Barnet in the second round on Saturday.
Rovers produced some magical moments in last season's competition, defeating Premier League sides Swansea City and Stoke City, before pushing Liverpool right to the wire in a quarter-final replay at Ewood Park, having held the Merseyside giants to a goalless draw at Anfield.
The third round draw in full:
Watford vs. Newcastle United
West Bromwich Albion vs. Bristol City
West Ham United vs. Wolverhampton Wanderers
Salford City or Hartlepool United vs. Derby County
Exeter City vs. Liverpool
Tottenham Hotspur vs. Leicester City
Colchester United vs. Charlton Athletic
Peterborough United vs. Preston North End
Northampton Town vs. MK Dons
Arsenal vs. Sunderland
Newport County vs. Blackburn Rovers
Ipswich Town vs. Portsmouth
Birmingham City vs. Bournemouth
Wycombe Wanderers vs. Aston Villa
Sheffield Wednesday vs. Fulham
Oxford United vs. Swansea City
Brentford vs. Chesterfield or Walsall
Bury vs. Bradford City
Manchester United vs. Sheffield United
Everton vs. Dagenham & Redbridge or Whitehawk
Southampton vs. Crystal Palace
Eastleigh vs. Bolton Wanderers
Nottingham Forest vs. Queens Park Rangers
Carlisle United vs. Yeovil Town
Chelsea vs. Leyton Orient or Scunthorpe United
Doncaster Rovers vs. Stoke City
Leeds United vs. Rotherham United
Cardiff City vs. Grimsby Town or Shrewsbury Town
Huddersfield Town vs. Reading
Middlesbrough vs. Burnley
Norwich City vs. Manchester City
Hull City vs. Brighton & Hove Albion