Creator-in-chief Christian Eriksen delivered a beautifully whipped cross and Llorente nipped in front of his man to glance the ball home.
Alli then saw his 51st minute effort deflect off target ahead of a risky tackle from Davinson Sanchez, who on a yellow card, was lucky not to be dismissed, before he was quickly withdrawn by Spurs boss Mauricio Pochettino in favour of Victor Wanyama.
"I think Harry doesn't have a price, because we want him here".
Spurs are seven points adrift of Liverpool with two matches in hand going into tomorrow's crucial encounter with Swansea.
Harry Kane's bid to become the first player in 71 years to score a hat-trick in three consecutive English league games could be ruined by illness.
However, Alli's 89th-minute effort ended Swansea hopes and Spurs secured a win that takes them back above Arsenal to fifth, while it proved to be a disappointing home debut for new Swansea coach Carlos Carvalhal.
Swansea looked to put Spurs on the back foot in the opening stages of the second half but failed to trouble Lloris. Jenkins must have been twitching nervously in his seat in the directors' box. Big decisions went against them and to rub salt in the wounds, Kane came off the bench to have his say with an assist. From the corner Mike van der Hoorn hit the post with a header. Substitutes: Luciano Narsingh (for Rangel, 53) 6, Oli McBurnie (for Dyer, 70) 6, Wayne Routledge (for Carroll, 78) 6.
South Korea worldwide Son, however, is a vital part of the Spurs camp and deserves more praise, according to Argentine boss Pochettino.
Victor Wanyama is also fit again after a long-term knee problem while Moussa Sissoko, Harry Winks and Serge Aurier will be involved against either West Ham or in Sunday's FA Cup tie with AFC Wimbledon.