England forward Daniel Sturridge and substitute Jordan Henderson spared Liverpool's blushes after their League One opponents stormed back to level at 2-2 after 90 minutes.
Hull City also advanced with a 1-0 extra-time win at Leyton Orient while Fulham won a penalty shootout 5-4 at League Two Burton Albion after their topsy-turvy showdown finished 2-2.
Bristol City upset top flight newcomers Crystal Palace 2-1 and Sunderland needed some late Connor Wickham heroics to snatch a thrilling 4-2 win over another League One side MK Dons.
Wickham scored twice and a set up a third in a breathtaking last 15 minutes as Sunderland turned around a two-goal deficit at the Stadium of Light.
West Bromich Albion's Saido Berahino netted a first half hat-trick in their 3-0 win over League Two Newport County while West Ham United held on to beat Cheltenham Town 2-1.
Southampton thrashed Barnsley 5-1 away and Norwich City enjoyed a 6-3 win over Bury in a goalfest at Carrow Road.
There are another seven second-round ties on Wednesday when Everton host Stevenage and Newcastle United visit Morecambe.
(Reporting by Tom Bartlett, Editing by Ken Ferris)
