The Southampton keeper made three fine stops as a new-look Charlton side containing five loan players - including two making their debuts - gave a much-improved performance which must have encouraged caretaker manager Phil Parkinson.
The first stop from Davis came after 16 minutes when he did well to hold on to Hameur Bouazza's stinging drive and then, with five minutes to go to the break, he palmed away a Keith Gillespie effort.
But two more saves right on half-time kept the score goalless at the break, with Bouazza again unluckily to see his effort stopped and then the best save of them all coming from an overhead kick from new boy Deon Burton.
Saints rarely threatened as an attacking force with Bradley Wright Phillips putting in their best effort over the bar.
The game was much more even in the second half as Charlton, low in confidence and failing to get that all-important first goal, began to run out of steam.
It was Charlton goalkeeper Nicky Weaver who had to show his agility by stopping a goalbound effort from David McGoldrick and then saving well from Matthew Paterson as Southampton sensed they could snatch victory.
Towards the end, Charlton brought on three substitutes as they searched for that elusive goal but, in the end, they had to be satisfied with a point.
They at least had the consolation of not conceding a goal for the first time in 13 matches, but they have now managed only one win in 14 games.
Meanwhile, Southampton are beginning to drag themselves away from the relegation zone as this was their second successive goalless draw.