The win lifts Spurs into seventh place in the table, and only three points off the top four, while Saints remain ninth.
Southampton opened the scoring after 13 minutes. Adam Lallana was allowed time and space on the edge of the Tottenham penalty area and found the bottom corner expertly.
The home side then threatened to run away with the game but Tottenham hit back when Roberto Soldado picked out Adebayor beautifully and the striker made no mistake, converting with a close-range volley.
After the break, Tottenham started the brighter and Jos Hooiveld knocked Danny Rose’s cross past his own ‘keeper.
Southampton responded, though, and Rickie Lambert sidefooted home after a superb reverse ball from Lallana.
Adebayor had the final word, however, smashing home a left-footed strike on 64 minutes after the ball fell to him in the box.
The victory will only boost Tim Sherwood’s chances of keeping the Tottenham job permanently.
Sherwood, Tottenham’s head of football development, was handed the role of interim manager in the aftermath of the dismissal of Andre Villas-Boas.
Saints, meanwhile, have now gone six matches without a win under reported Spurs target Mauricio Pochettino.
Counterpart Pochettino made three changes and his injury-hit side had the first chance of the afternoon inside three minutes, with a long-range Lambert free-kick beating the wall but not Lloris.
The next strike on Tottenham’s goal, though, was too good for the Frenchman.
Danny Fox burst forward and fed Lallana, who turned Vlad Chiriches on the edge of the box before firing a low strike into the bottom corner.
A wayward attempt from Gylfi Sigurdsson was the only shot Tottenham mustered in the opening 20 minutes and perhaps led to Sherwood’s decision to swap his vantage point in the directors’ box for the technical area.
He was somewhat fortunate not to see his side go further behind soon after he made it pitchside as Southampton’s England trio linked up superbly.
Lambert was allowed time to cut the ball across for Lallana, whose fine touch played through Jay Rodriguez, although he was unable to direct his effort on target.
It was a missed opportunity Saints were made to rue in the 25th minute as rejuvenated Adebayor struck home, with Soldado keeping his wayward pass in and swinging over a cross which the striker turned home with a superb hooked volley.
Spurs ended the half in the ascendancy and continued in the same manner when play resumed, although injury meant Mousa Dembele soon had to be replaced by 19-year-old debutant Nabil Bentaleb.
Despite the enforced alteration, the visitors remained on top and it was no surprise when they went ahead in the 54th minute.
Christian Eriksen played through Rose, whose low cross from the left was directed home by Hooiveld. It was a comical own goal that had the 3,173 away fans in fine voice – if only for five minutes.
Jack Cork played a defence-splitting pass through to Lallana and, with Lloris having rushed off his line, the Saints captain squared for Lambert to put into the empty net.
After doing well to prevent Adebayor putting Spurs back ahead, Paulo Gazzaniga was soon beaten by the former Arsenal striker after calamitous defending from a quick throw-in allowed him to strike home.
Further chances followed for Spurs as first Soldado burst clear on goal and somehow put wide, before then meeting a fine cross from the right but hitting a six-yard strike into the ground and over.
Spurs’ next assignment is at home to West Brom on Boxing Day, when Saints travel to Cardiff.