Rafa Benitez’s side went on to lift the trophy that season, defeating West Ham on penalties in Cardiff after a 3-3 draw – rescued by Steven Gerrard’s 40-yard stoppage time strike.
That seemed a long way off when they trailed to Luton at Kenilworth Road, 3-1 at one point.
Two goals each for Florent Sinama Pongolle and Alonso, plus Gerrard’s earlier converted penalty, saw them through.
Liverpool: Carson, Finnan, Hyypia, Carragher, Riise, Kewell, Gerrard, Sissoko (Sinama Pongolle 57), Alonso, Crouch (Kromkamp 79), Cisse (Warnock 89).
Subs Not Used: Hamann, Reina.
Goals: Gerrard 16, Sinama Pongolle 62, Alonso 69, Sinama Pongolle 74, Alonso 90.