The former Swansea City target man marked his maiden Premier League start in our colours following his summer move from south Wales with an early breakthrough from Christian Eriksen's free-kick.
It was also the Spaniard's first domestic goal for us and came amid a spell of intense first-half pressure in the driving rain, but it took until the 89th minute for us to find a second through Dele Alli.
We'd dominated the play without really creating any clear chances but when substitute Harry Kane picked out his fellow England international with a delightful cross-field pass, the midfielder pinged into the top corner at the second time of asking after initially being denied by Lukasz Fabianski.
It served to put the game beyond doubt as, despite our command of the ball, the home side put up more of a fight after the interval and went close twice in a minute as Jordan Ayew skipped through on goal before the returning Victor Wanyama swept behind, with Tom Carroll's resulting corner striking Jan Vertonghen's back and hitting the post.
In the end, it was job done and maximum points recorded ahead of a home clash with West Ham United on Thursday night.
Mauricio Pochettino made four changes to the team that started against Southampton last time out on Boxing Day, but it was the inclusion of midfielder Wanyama among the substitutes that was the biggest cause for cheer before kick-off as he was named in the matchday squad for the first time since August after recovering from a knee injury. Kane joined him on the bench after suffering from illness since the Saints clash with Llorente taking his place. Both were introduced to important effect in the second period. Elsewhere, Kieran Trippier, ex-Swansea man Ben Davies and Erik Lamela came in for Serge Aurier, Danny Rose and Mousa Dembele, the latter two missing out with knee and hip injuries respectively. Our former midfielder Carroll started for the Swans, replaced in the second half by winger Wayne Routledge, but full-back Kyle Naughton missed out through suspension.
GOAL: SWANSEA 0-1 SPURS - FERNANDO LLORENTE - 12mins
Who else to open the scoring but Llorente on his first return to the Liberty Stadium in our colours? After Heung-Min Son was upended by Carroll out wide on our left, Christian Eriksen delivered the set piece and Llorente shook off his marker to glance in a header at the near post. The striker's celebrations were understandably subdued out of respect for his former club. Llorente might have doubled his tally from another Eriksen set-piece shortly before half-time but his outstretched leg sent the ball looping just over the bar.
Above: Fernando Llorente competes with Tom Carroll.
CHANCE: AYEW SKIPS FREE IN THE BOX - 69mins
It had been one-way traffic in the first period but Swansea were starting to mount some attacks as the game wore on and after substitute Luciano Narsingh forced a save from Hugo Lloris at his near post and Dele headed wide despite appearing to be on the receiving end of a push from Mike van der Hoorn at the other end, they had a big chance on 69 minutes. Ayew skipped in from the left, rounded Lloris as he dived at his feet and then evaded the challenge of Davies before Wanyama steamed in to sweep behind.
WOODWORK: POST SPARES VERTONGHEN'S BLUSHES - 70mins
From the corner conceded by Wanyama, Carroll whipped in a dangerous ball that hit Vertonghen on the back as he tried to contain Van der Hoorn and deflected onto the post. Thankfully, we cleared our lines from there, but the Swans were looking more dangerous.
GOAL: SWANSEA 0-2 SPURS - DELE - 89mins
Son fired across goal but just wide after getting on the end of a trademark Trippier delivery at the back post with 12 minutes left, but we wrapped things up on 89 minutes. Kane battled down the left before spotting Dele in space on the other side and playing a superb pass to the midfielder, who advanced on goal and saw his shot repelled by Fabianski. The quick-thinking star adjusted his feet in a flash and rifled the rebound into the top corner.
MAURICIO POCHETTINO SAID
"The conditions were difficult and for the players, horrible. We played well and deserved the victory overall. The conditions weren't the best to play football but we tried to play our football and the effort was fantastic. Now we need to recover quickly and be ready to play against West Ham."
FERNANDO LLORENTE SAID
"I'm very happy to score my first goal in the Premier League for Tottenham and help the team. It was a difficult game in difficult conditions but the important thing was we were focused and aggressive. We wanted to play and move the ball quickly. We controlled the game and played really well, especially in the first half. There was no pressure on me (coming in for Harry Kane) - for me, it was an amazing opportunity."
Swansea City (3-5-2): Fabianski, Van der Hoorn, Fernandez, Mawson, Rangel (c, Narsingh 53), Clucas, Carroll (Routledge 78), Sanches, Olsson, Dyer (McBurnie 70), Ayew. Substitutes (not used): Nordfeldt, Bartley, Roque Mesa, Fer.
Spurs (4-2-3-1): Lloris (c), Trippier, Sanchez (Wanyama 59), Vertonghen, Davies, Dier, Eriksen, Lamela (Sissoko 76), Dele, Son, Llorente (Kane 68). Substitutes (not used): Vorm, Aurier, Walker-Peters, Winks.
Goals: Spurs - Llorente 12, Dele 89.
Yellow cards: Swansea - Olsson 10, Van der Hoorn 79; Spurs - Sanchez 31, Lamela 64.
Referee: Robert Madley.
MAN OF THE MATCH
Dele was named Man of the Match with 42 per cent of fans' votes on social media.
It's a quick turnaround as we get set for a London derby with West Ham United at Wembley injust 48 hours' time. Kick-off on Thursday night is at 8pm. The Hammers secured a last-gasp 2-1 win at home to West Bromwich Albion on Tuesday night, putting them 16th in the Premier League table.