Danny Graham's first-half strike booked Blackburn a third-round home tie with Hull after they overcame Sky Bet League Two strugglers Crewe 1-0.
With the game played 24 hours after it was originally scheduled due to a frozen pitch at Gresty Road on Tuesday, Graham scored the only goal of the game in the 24th minute.
A Rovers side showing six changes from weekend League One duty were the first to pose a threat when one of those players coming into Tony Mowbray's ranks, 20-year-old striker Joe Nuttall glanced a header over.
Rovers were soon ahead when Graham glided across the snow-flecked surface to angle Derrick Williams' pass into the bottom corner.
Veteran Graham was close to nabbing a second soon after when his stinging drive flicked off the upright.
Unlike in the first game where they let a three-goal lead slip, Blackburn were always in control and Sam Hart was denied by a combination of goalkeeper Ben Garratt and defender Eddie Nolan after he burst past his marker.
Crewe had barely mustered a threat but were agonisingly close to levelling on the hour mark when Chris Dagnall's header thudded against the post after substitute Charlie Kirk sent in a tantalising cross.
But Nuttall should have sealed the tie, only to poke wide after Nolan's sliced clearance was diverted into his path by Garratt.