Non-league Havant and Waterlooville put in a superb first-half performance as they twice took the lead at Anfield but Liverpool responded to leave the scores locked at 2-2 at half-time.
The Blue Square Conference South side, ranked 123 places below their Barclays Premier League opponents, took a surprise lead in the eighth minute after Richard Pacquette headed a Mo Harkin corner past goalkeeper Charles Itandje.
The lead lasted 19 minutes before Liverpool midfielder Lucas Leiva levelled with a 25-yard strike which flew past Havant goalkeeper Kevin Scriven and into the top-right corner of the net.
Remarkably, Havant took the lead again in the 31st minute when Alfie Potter’s shot was directed past Itandje by Martin Skrtel.
But Yossi Benayoun equalised a minute before the break with an 18-yard finish.
Coca-Cola Championship side Preston held a 3-0 interval lead over Premier League side Derby at Pride Park.
Karl Hawley capitalised on a mistake by defender Andy Todd in the 14th minute with a close-range finish and Simon Whaley doubled the advantage in the 33rd minute before Hawley made it 3-0 on the stroke of half-time.
West Brom held a 2-0 lead over Peterborough at London Road thanks to a Roman Bednar tap-in and a close-range finish from Robert Koren after a swift counter-attack.
Stephen Hughes gave Coventry the lead at home to Millwall when he smashed home a free-kick in the 16th-minute – but Jay Simpson equalised for the visitors moments before the break.
A 10th-minute header from Luke Beckett gave Huddersfield a first-half lead over League One rivals Oldham at Boundary Park.
Portsmouth came back from a goal down to lead Plymouth 2-1 at Fratton Park.
Chris Clark put Plymouth ahead in the fifth minute with a low shot which took a deflection off Hermann Hreidarsson and deceived Pompey goalkeeper David James.
But Lassana Diarra equalised in the 34th minute and Niko Kranjcar put the Barclays Premier League side ahead in the 45th minute.
Wolves held a one-goal lead over Watford at Vicarage Road thanks to Andy Keogh’s goal in the fifth minute.
League Two Barnet and League One Bristol Rovers were scoreless at the midway mark at Underhill, with the home side’s Jason Puncheon missing a penalty in first-half injury-time.
In the day’s early kick-off Middlesbrough claimed a hard-fought 2-0 win over Mansfield thanks to a first-half strike from Dong-Gook Lee and a late own-goal from Jake Buxton.