Strikes in either half from Lee Holmes and David McGoldrick put the Saints in complete control before a late strike from Dean Moxey put the Grecians back in the tie.
It was a tense finish but McGoldick wrapped it up for the Championship side with a penalty deep into injury time.
Midway through the half, the Championship side took the lead when former Plymouth Argyle captain Paul Wotton beat the offside trap and laid the ball back to Holmes, who rifled a shot into the roof of the net from just inside the box.
Southampton had goalkeeper Bartosz Bialkowski to thank for an excellent double save just before the break.
Ryan Harley found himself free inside the box and forced Bialkowski to save well and again from Adam Stansfield's rebound.
Exeter again came close to pulling level shortly after the restart. Stansfield had a shot saved by Bialkowski and Marcus Stewart headed Steve Tully's cross over the bar in the opening minutes.
The ever-dangerous Holmes again when close when he burst into the box but he was denied by Matt Taylor's lunging tackle.
Stern John was introduced a touch of class to the proceeding as the Saints began to stretch Exeter.
With 15 minutes left, Wotton's fine ball picked out McGoldrick and the striker skipped past two players before burying a low shot past Jones.
Substitute Moxey bundled in a close-range strike for the Grecians from Tully's throw with four minutes left to set up a grandstand finish.
But in injury time, Danny Seaborne brought down McGoldick, who picked himself up to score from the spot.