Manchester United laboured against Northampton until Marcus Rashford was introduced and made one assist and scored United's third to send Mourinho's men into the last-16 of the competition.
Manchester City maintained a 100% start to the season and Dimitri Payet scored in added time to give West Ham a narrow victory over Accrington Stanley.
EFL Cup results, 21 September
Fulham 1-2 Bristol City
Northampton Town 1-3 Manchester United
Queens Park Rangers 1-2 Sunderland
Southampton 2-0 Crystal Palace
Swansea City 1-2 Man City
West Ham United 1-0 Accrington Stanley
Stoke City 1-2 Hull City
Tottenham Hotspur 5-0 Gillingham