Unexpectedly, Jerzy Dudek was selected in goal, with Chris Kirkland not even on the bench.
The Polish keeper made several good blocks as Biscan and Vignal struggled in defence.
The Tractor Boys took the lead in the 13th minute but a penalty from El-Hadji Diouf in the 53rd minute levelled the game, which went into extra time then penalties.
Steven Gerrard, Milan Baros, John Arne Riise, Jamie Carragher and Diouf all scored their penalties to put the Reds through to the next round where they will face Aston Villa.
Liverpool: Dudek, Xavier, Biscan, Babbel, Vignal, Riise, Gerrard, Diao, Smicer, Diouf, Mellor. Subs: Baros, Arphexad, Carragher, Welsh, Otsemobor.
Ipswich: Marshall, Gaardsoe, Venus, Hreidarsson, Wright, Miller, Holland, Ambrose, Clapham, Darren Bent, Counago. Subs: Wilnis, Magilton, Armstrong, Naylor, Pullen.
Referee: D Gallagher