Rashford stepped off the bench to fire two late goals to put the seal on an eighth victory in a row in all competitions for the home side.
A summary of Saturday's action in the FA Cup.
Premier League sides Manchester United and Aston Villa reached the fourth round of the FA Cup on Sunday after seeing off lower league opponents Southampton and Gillingham.
Premier League clubs West Bromwich Albion and Watford were knocked out in the League Cup second round by lower-league opponents on Tuesday as a strong Liverpool side crushed championship Burton Albion 5-0.
Manchester City continued their imperious start to the season with a 2-1 win over Swansea City to reach the fourth round of the League Cup on Wednesday but it was a testing night for rivals United who eventually overcame Northampton Town 3-1.
Manchester United will travel to third-tier MK Dons in the Capital One Cup second round following the draw on Wednesday, the first time they have been involved at this stage of the competition for 19 years.
Prince Louis, the youngest child of United Kingdon's Prince William and Kate, was christened on Monday (July 9), at the Chapel Royal in London with family by his side.
Images from the FA Cup matches played on Saturday
Chelsea midfielder Cesc Fabregas gave his manager a reminder of his talents by scoring twice in extra time as they fought back from two goals down to knock Premier League champions LeicesterCity out of the League Cup 4-2 on Tuesday.
News of all that transpired on and off the football field on Friday
News of all that's transpired on and off the football field
Manchester United's early season problems were compounded by a humiliating 4-0 loss to third-tier Milton Keynes Dons in the League Cup second round on Tuesday leaving new manager Louis van Gaal still looking for his first win.
Former Russian spy Sergei Skripal, 66, and his daughter Yulia, 33, were found collapsed after being poisoned last week. Both remain in a serious condition along with a police officer who came in contact with the same substance.