It was Webb who opened the scoring on 19 mins with a header. Peter Whittingham scored with a free kick on 37 mins to make it 2 - 0 to City at half time.
Within 5 mins of the restart City were 4 - 0 up. Whittingham and then Thompson both scored in the opening minutes of the seasond hald.
Northampton's consolation came from Shaun Goodhall on 51 mins.
City fielded a side that included keeper David Forde, Darren Purse, Kevin Cooper and scorers Whittingham and Thompson.
Northampton Town: Guest, Danny May, Freddie Avill, Alex Dyer, Nick Thorogood, Brett Johnson, Greg Taylor, Joe Burnell, Shaun Goodall, Ryan Gilligan, Joe Benjamin.
Cardiff City: David Forde, Chris Gunter, Darren Purse, Anthony Anchenpong, Ashley Buswell, Kevin Cooper, Peter Whittingham, Aaron Ramsey, Darcy Blake, Steven Thompson, Terrell Webb.