His goals came after Djamel Belmadi had put Southampton ahead after just nine minutes.
If it had not been for some outstanding saves by Antti Niemi, the Norwich victory might have been even more emphatic because the Canaries were in command for most of the game.
The Saints kicked off attacking the River End goal and Danny Higginbotham brought a diving save from Robert Green inside the first three minutes.
In the ninth minute the visitors went ahead. David Prutton crossed from the left and Belmadi's low left-foot shot squirmed under Green.
Norwich battled back and Gary Doherty's header was turned around the post by Niemi in the 20th minute.
Darren Huckerby and Andy Hughes went close with shots before Ashton scored the equaliser after half an hour with a precise near-post header from Huckerby's in-swinging cross from the left.
Youssef Safri's free-kick only just missed the target before the unfortunate Hughes was stretchered off two minutes before half-time with a fractured cheek bone. He was replaced by loan signing Dickson Etuhu.
In first-half stoppage time Paul McVeigh headed over from close range.
Three minutes into the second half David Wright's cross was cleared off Ashton's toe when he looked certain to score.
He had better luck on 51 minutes when he met Safri's right-wing corner with a firm header from 10 yards which flew inside the far post.
He then set up McVeigh on the edge of the area, but Niemi made an acrobatic save to keep out his chip and Huckerby fired over when he pounced on the loose ball.
Niemi then made a brilliant double save to deny Etuhu and then palmed Ashton's shot over the bar before blocking further shots from both Ashton and Huckerby in quick succession.
However, Ashton was not to be denied and completed his hat-trick after 66 minutes.
Following Safri's right-wing corner a shot with his left foot was blocked by a defender, but he reacted quickly and hit a right-foot volley from close range that gave Niemi no chance.