Davis made a mistake for Torquay's opening goal in the Johnstone's Paint Trophy clash at St Mary's and then conceded a penalty for their second as the League Two strugglers surged into a 2-0 half-time lead.
The Gulls went ahead in the 20th minute when Davis mistimed a punch when Kevin Nicholson propelled a long throw into the Southampton box. Davis succeeded only in pushing the ball against Tim Sills whose header ricocheted into the net.
Torquay's second came in the 41st minute when Davis brought down Tyrone Thompson in the box to concede a penalty and was fortunate only to get a yellow card.
Nicky Wroe converted the spot-kick but Southampton staged a storming second-half rally. They pulled a goal back in the 59th minute when Papa Waigo forced the ball over the line following a Dan Harding free-kick and then Waigo got Southampton's equaliser in the 69th minute with another close-range effort.
Southampton converted all of their penalties but the crucial moment came at 3-2 when Davis plunged to his left to keep out Nicholson's effort and it was enough to see a ragged Saints through.