Tottenham remain on the winning trail ahead of two more games in the next five days, but Swansea will complain that they did not get the benefit of the decisions tonight.
It took Llorente only 12 minutes to regain his goalscoring touch on his old stomping ground, as he headed home a Christian Eriksen set piece at the near post.
However, the assistant referee failed to spot that the Spaniard, who scored 15 goals for Swansea last season, had drifted several yards offside in getting goalside of Federico Fernandez.
Tottenham completely dominated for the opening half an hour, but a combination of a deep Swansea backline and the wet and blustery conditions made it difficult for them to create chances.
Their only other opportunity of the first half came when Alli dragged a half-volley wide from Llorente's layoff on 23 minutes.
The home crowd were buoyed by the sense that the puddled surface was beginning to even the playing field, and Swansea finally created an opening when Angel Rangel's cross landed at Martin Olsson's feet, only for the Swede to slice a shot wide of Hugo Lloris's near post on 41 minutes.
Eriksen and Llorente nearly linked up for Spurs again before half time, but the striker opted to go with a stretched boot rather than a header and could not control an effort which flew over the crossbar.
Although Swansea were slightly more progressive after the break, they still did not possess much of a goalscoring threat, and yet were denied a route back into the game when Davinson Sanchez survived what appeared to be a blatant second yellow card for a foul on Jordan Ayew on 55 minutes.
The teams exchanged chances after the hour mark as Lukasz Fabianski saved from an Eriksen free kick, and Lloris blocked bravely at his near post after Renato Sanches released substitute Luciano Narsingh.
Swansea twice came close to an equaliser in the 70th minute, when Ayew rounded Lloris only to see his shot blocked, and Mike van der Hoorn headed against the frame of the goal from Tom Carroll's corner.
Kane came off the bench to supply Tottenham's second with an inch-perfect assist for Alli, who saw his initial effort saved by Fabianski but adjusted his feet quickly to convert the rebound on 89 minutes.
The result sees Tottenham climb above rivals Arsenal into fifth in the table, while Swansea remain bottom after a first defeat under new manager Carlos Carvalhal.
SWANSEA (5-3-2): Fabianski; Rangel (Narsingh, 53'), Van der Hoorn, Fernandez, Mawson, Olsson; Carroll (Routledge 78', Clucas, Sanches; Dyer (McBurnie, 71'), Ayew
TOTTENHAM (4-1-4-1): Lloris; Trippier, Sanchez (Wanyama 59'), Vertonghen, Davies; Dier; Son, Eriksen, Alli, Lamela (Sissoko, 77'); Llorente (Kane 68')