The Saints began brightly and grabbed an early lead when Djamel Belmadi fired in from 12 yards out.
Ashton then nodded in the equaliser as the home side started to dominate but they suffered a setback when Andy Hughes came off with a serious injury.
However, the Canaries continued to press forward and Ashton planted a firm header past keeper Antti Niemi before grabbing his third with a fine volley.
Southampton caretaker boss Dave Bassett:
"Our keeper Antti Niemi did very well in the second half and pulled off some excellent saves off.
"Had it not been for him I think the scoreline could have been even more.
"Antti was our best player and that is unusual. We had so many players that came second best and that normally does not happen."
Norwich: Green, Wright, Fleming, Doherty, Drury, Hughes (Etuhu 43), Safri, Robinson, Huckerby (Charlton 90), Ashton, McVeigh (McKenzie 74).
Subs Not Used: Ward, Henderson.
Goals: Ashton 30, 51, 66.
Southampton: Niemi, Cranie, Kenton, Powell, Higginbotham, Belmadi (Ormerod 67), Prutton, Oakley, McCann, Walcott (Best 55), Jones (Fuller 54).
Subs Not Used: Smith, Kosowski.
Booked: Cranie, Powell, Higginbotham.
Goals: Belmadi 9.
Ref: T Bates (Staffordshire).