Billy Sharp finally got off the mark with two lethal strikes to kill off Morecambe's cup dreams as he paid back the first instalment of his £2million transfer fee for the Blades.
The 21-year-old, signed from Scunthorpe in the summer, struck in the first half with Luton Shelton grabbing two and midfielder Lee Hendrie scoring his first for the side since his move from Aston Villa.
Blackpool continued their habit of being involved in last-ditch finishes when Michael Jackson saw them through a difficult tie with a 118th minute winner against League One Southend.
The match was just six minutes old when Rhys Evans' badly timed lunge at Charlie MacDonald's legs saw Southend awarded a penalty which Matt Harrold converted.
It took the arrival of Blackpool's Irish talisman Wes Hoolahan to change the course of the game.
His darting run into the box in the 80th minute ended with two blocked shots before Scott Vernon forced the ball home from a narrow angle.
The game moved into extra-time with Collis earning his wages at last with two great stops from Andy Morrell and Jackson.
Jackson was causing problems at all the set pieces and, when Southend failed to clear a Hoolahan corner, the experienced defender slammed the ball in at the far post for the latest of late winners.
Golden oldies Robbie Fowler, Jimmy Floyd Hasselbaink and Trevor Sinclair tore West Bromwich Albion apart to fire Cardiff City into the last 16.
Fowler netted twice, once from the spot, with his fellow veterans scoring one apiece.
Burnley bowed out with a 1-0 home defeat to top flight Portsmouth, while Norwich and Charlton were defeated by Manchester City and Luton Town respectively.