Northampton continued their dominant performance at the start of the second half, as the visitors put Luther Burrell in for their third try of the game.
The Exiles had a chance to get back into the match late on, as Alex Waller was sent to the sin bin, leaving the visitors a man short.
Daniel Browne secured the hosts' second try of the afternoon, reducing Northampton's lead to 10, but Welsh were unable to reduce the deficit further, with Gordon Ross finishing the game in the sin bin.
Burrell completed his brace late on, securing a bonus point for Northampton.
The result keeps Saints clear of fifth-placed Gloucester, while the Exiles remain 12 points adrift at the bottom of the table.