United will face Robert Di Matteo's side at Stamford Bridge for a place in the quarter-finals after goals either side of half-time from Anderson and Tom Cleverley downed Newcastle, who could not find an equaliser despite substitute Papiss Cisse scoring with a header on 62 minutes.
Liverpool manager Brendan Rodgers will face his former club Swansea at Anfield after a 2-1 win over West Bromwich Albion was inspired by a Nuri Sahin double (17,82) to cancel out Gabriel Tamas's opening goal on three minutes.
Reading host Arsenal - 6-1 winners against Coventry City - while Norwich City meet Tottenham in other all-Premier League ties.
There is a North-East derby between Sunderland and Middlesbrough while Aston Villa visit League One Swindon Town in the last 16 after their surprise 4-2 win over Premier League champions Manchester City on Tuesday night.
Elsewhere, Leeds United will try to emulate their 2-1 win over Everton when they host Premier League Southampton. Wigan Athletic appear to have been handed the most favourable draw in the shape of a home tie against League Two Bradford City, who eked out a 3-2 win against Burton Albion after extra-time on Tuesday night.
Capital One Cup
Fourth-round draw (ties to be played on week commencing October 29)
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