Michael Carrick put United ahead but Northampton equalised before half time through an Alex Revell penalty.
But Ander Herrera and Marcus Rashford sealed the win.
West Ham were within seconds of being taken to extra time by League Two Accrington before Dmitri Payet’s free-kick settled the tie in the 96th minute.
No problems for Spurs as they thrashed Gillingham 5-0, while Sunderland came from behind to beat QPR 2-1.
More concerns for Stoke as they were beaten 2-1 at home by Hull, while the other all-Premier League tie saw Southampton beat Crystal Palace 2-0.
In the night’s other tie Bristol City won 2-1 at Fulham.