Spurs, who are in danger of losing their grip on second spot, went into the match having seen their title aspirations ended by Chelsea last time out, but they started well and were ahead early on through Son Heung-min.
Davis pegged them back with a simple finish from close range, while Shane Long missed an early second-half chance to put the visitors ahead.
It mattered little, though, as Davis placed a low effort beyond Lloris to complete their comeback and deliver another blow to Spurs' chances of surpassing their best BPL points total of 72.
Defeat means Mauricio Pochettino's side need to beat Newcastle United on the final day to move on to 73 points and guarantee their place in the top three, without having to rely on other results.
With plenty on the line for both sides the contest began at a frantic pace and the impressive Christian Eriksen was immediately to the fore, the Denmark international testing Fraser Forster in the fifth minute.
Having soaked up the early Spurs pressure, Southampton – unchanged from their win over Manchester City – enjoyed success on the counter-attack, with Dusan Tadic and Ryan Bertrand flashing low crosses across Lloris' goal.
Harry Kane and Eriksen both passed up chances to double Spurs' advantage and they were made to pay as Davis levelled just after the half hour, the midfielder converting Tadic's pass from close range.
The home side – who recalled Ryan Mason for the suspended Mousa Dembele – might have been back in front by the break, but Forster was on hand to deny Kane in stoppage time.
Long was presented with a glorious chance from Tadic's pinpoint cross nine minutes after the restart as the Republic of Ireland international rose above Danny Rose, but failed to get enough on his header.
Pochettino's men pushed for an equaliser in the closing minutes, but Kane and Erik Lamela were wasteful and Nacer Chadli was brilliantly denied by Forster as Southampton clung on for the win, moving them on to 60 points – equalling their club record set last season.
