After being held to a draw by the League One outfit ten days ago, Ian Holloway's side showed their superiority by taking a seventh-minute lead.
Lua Lua then got himself on the scoresheet with a curling effort from 25 yards to double the Seasiders' advantage.
Blackpool were in control from then on, and when Ludovic Sylvestre added a third ten minutes into the second half the visitors had all but secured their place in the next round.
The former Barcelona player linked up with Phillips before cutting inside and firing a shot past Bywater.
Blackpool travel to Goodison Park for their last-16 tie against the Toffees on February 18.