Nuri Sahin's 82nd minute winner against West Brom at the Hawthorns on Wednesday secured the Reds' passage, while Swansea came from 2-1 down to dump out League One Crawley Town on Tuesday.
Manchester United, meanwhile, face a tricky trip to Stamford Bridge to meet Chelsea after they edged past Newcastle 2-1 at Old Trafford. The Blues are in ominous form after booking their place in the last 16 with a crushing 6-0 victory over Wolves on Tuesday.
Arsenal also hit League One strugglers Coventry for six, with Theo Walcott netting twice, and have been rewarded with a trip Reading. Their north London rivals Tottenham face Norwich City at Carrow Road.
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Neil Warnock's Leeds shocked Everton with a 2-1 win at Elland Road on Tuesday night and they will meet Premier League opposition at home again in the form of Southampton.
Swindon Town have beaten top-flight opponents at the County Ground in Stoke and they will be hoping to do the same when they welcome Aston Villa, who knocked out Manchester City on Tuesday.
League Two high-fliers Bradford are the lowest ranked team left in the competition and they travel to Wigan Athletic after coming from 2-0 down to beat Burton Albion 3-2 in extra time.
Fourth Round draw in full
Sunderland v Middlesbrough
Swindon Town v Aston Villa
Wigan Athletic v Bradford City
Leeds United v Southampton
Norwich City v Tottenham Hotspur
Liverpool v Swansea City
Chelsea v Manchester United
Reading v Arsenal