It was a big win for Manchester City as they put four past visiting Burnley while Millwall also flogged Barnsley 4-1 in their FA Cup third round encounters on Saturday.
Preston North End were also on song as they hit Wycombe Wanderers for five.
Here are the results of matches played so far:
Liverpool 2 -1 Everton
Manchester United 2-0 Derby County
Fleetwood Town 0-0 Leicester City
Middlesbrough 2-0 Sunderland
Aston Villa 1-3 Peterborough United
Birmingham City 1-0 Burton Albion
Blackburn Rovers 0-1 Hull City
Bolton Wanderers 1-2 Huddersfield Town
AFC Bournemouth 2-2 Wigan Athletic
Brentford 0-1 Notts County
Cardiff City 0-0 Mansfield Town
Carlisle United 0-0 Sheffield Wednesday
Coventry City 2-1 Stoke City
Doncaster Rovers 0-1 Rochdale
Exeter City 0-2 West Bromwich Albion
Fulham 0-1 Southampton
Ipswich Town 0-1 Sheffield United
Manchester City 4-1 Burnley
Millwall 4-1 Barnsley
Newcastle United 3-1 Luton Town
Queens Park Rangers 0-1 Milton Keynes Dons
Stevenage 0-0 Reading
Watford 3-0 Bristol City
Wolverhampton Wanderers 0-0 Swansea City
Wycombe Wanderers 1-5 Preston North End
Yeovil Town 2-0 Bradford City