However, with one of their first meaningful efforts on goal, Southampton took the lead in the 27th minute. The Portsmouth defence failed to pick up Billy Sharp inside the area and the former Doncaster Rovers frontman struck from inside the area.
The home side's lead only lasted nine minutes though, as Chris Maguire bent the ball beyond the reach of Davies and into the top corner of the net.
Both sides created openings after the restart to take the lead, but both found getting their efforts on target a challenge.
Just as it looked as though the match would end 1-1, Sharp converted his second of the match from close range following a cross from strike partner Rickie Lambert for looked to be the winner.
Norris had other ideas though, as he shot into left-hand corner of the net from outside the area with one minute of injury time remaining.
Southampton are now ahead of Reading on goal difference.