Holders City, who have won two of the last three League Cups, clinched a ninth straight win in all competitions under Pep Guardiola as goals from Gael Clichy and 19-year-old Aleix Garcia helped them through an all-Premier League encounter at the Liberty Stadium.
It was far less straightforward for United, who were pegged back and frustrated by third tier Northampton before goals from Ander Herrera and Marcus Rashford wrapped up the win.
The two Manchester rivals were then paired against each other in the fourth round draw that also pitched Liverpool against Tottenham Hotspur and West Ham United against Chelsea.
Tottenham made light work of third tier Gillingham, romping to a 5-0 victory, while West Ham needed a 96th-minute free kick from Dimitri Payet to beat Accrington Stanley 1-0.
City and United both began the season strongly but while Guardiola's side have gone from strength to strength United's good early form has disappeared and they came into the clash against Northampton on the back of three straight defeats.
City looked in control of their tie against Swansea from the start and took the lead when Clichy ended a flowing move with a right-footed effort four minutes after halftime.
When Garcia steered home Jesus Navas's cross midway through the second half the tie was effectively done and dusted although Swansea scored a stoppage-time consolation through Gylfi Sigurdsson.
It was a different story at Northampton's tiny Sixfields stadium, where United dominated the ball but looked edgy and nervous after Michael Carrick's powerful opener was cancelled out by Alex Revell's penalty just before halftime.
The home side then frustrated the visitors with a resilient defensive display until Herrera lifted the tension for United's travelling fans with a rifled effort from distance and Rashford capitalised on a goalkeeping blunder to walk the ball into the net.
"It was difficult as I was expecting but we looked to be in control for the first 35 minutes and then we looked to be in control for the last 45," United boss Jose Mourinho told Sky Sports.
Tottenham, who made 11 changes from the side that beat Sunderland on Sunday, brushed aside Gillingham with ease as Christian Eriksen opened the scoring with a stunning effort from distance and then doubled the lead.
Dutch striker Vincent Janssen netted his first for the club from the penalty spot and further goals Erik Lamela and Josh Onomah rounded off the romp against a Gillingham side managed by former Spurs player Justin Edinburgh.
West Ham, who have lost four of their five opening Premier League games, were locked in stalemate and heading for extra time against fourth division Accrington Stanley before Payet lined up a free kick deep into stoppage time.
The France international, who started on the bench, bent the ball over the wall to beat Accrington keeper Elliot Parish.
Charlie Austin and Jake Hesketh were on target for Southampton as they beat Crystal Palace 2-0 in an all-Premier League tie while Sunderland's Paddy McNair scored twice in a 2-1 win over Championship side Queens Park Rangers.
Hull City booked their spot in the next round after coming from behind to beat struggling Stoke City 2-1 thanks to a stoppage-time winner from Markus Henriksen. Bristol City beat Fulham 2-1.
(Reporting by Toby Davis, editing by Pritha Sarkar)
source: www.abs-cbnnews.com
