- Daniel N'Lundulu (17')
- James Ward-Prowse (89')
The victory means the Saints will face Arsenal at home in the fourth round on Saturday.
N'Lundulu, making his debut for the club, opened the scoring in the sixth minute after the Shrewsbury defence failed to deal with a high ball into the box.
Ward-Prowse wrapped up the win for a Southampton side that had made a number of changes, with a free kick.
The match was originally scheduled for Jan. 9 but was called off after a coronavirus outbreak at the League One club and manager Steve Cotterill is still in hospital after testing positive.