Swansea took the lead through Llorente, latching onto Gylfi Sigurdsson’s deep free-kick before Jordan Pickford could claim the cross.
Naughton then doubled the lead with his first ever Premier League goal just before half-time, racing on to Ki Sung-Yeung’s pass before firing past Pickford.
First half dominated by the away side
The first chance of the game fell to Didier Ndong after seven minutes, the ball fell to the midfielder on the edge of the box after some desperate defending, but he was only able to hit the side netting with his shot.
Swansea took the lead just moments later, Llorente scoring yet another huge goal after a deep free-kick by Sigurdsson.
Pickford came a long way to try and claim the cross, but Llorente met the ball first and the Spaniard was able to score his 14th league goal of the season.
This was Llorente’s seventh headed goal of the season, more than any other Premier League player this season.
Another assist for Sigurdsson saw him notch up his eighth of 2017, more than any other Premier League player.
After some early fight, Swansea started to enjoy a spell of dominance over Sunderland, who seemed a different team from the one that went to Hull and won last week.
Lukasz Fabianski was then quick off his line to deny Jermaine Defoe an equaliser and what would be his sixth goal in his last five games against Swansea.
Naughton then doubled Swansea’s tally with his first goal in 141 Premier League games, picking the ball up from Ki, sizing up Javier Manquillo before smashing the ball past Pickford.
Drab second half
Sunderland came out a bit brighter after half-time, but still weren’t really doing enough to trouble Swansea.
The away side did look a tad complacent in the second-half, something manager Paul Clement surely won’t be happy with.
Former Swansea loanee Fabio Borini had an effort deflected onto the post after 65 minutes, the first real effort of the second-half.
A minute later, substitute Wahbi Khazri volleyed an effort from 25 yards on goal but didn’t catch the ball as cleanly as he would have liked and Fabianski was on hand to stop the effort.
Swansea appeared happy to sit back on their two-goal lead and allow Sunderland to attack them, knowing perhaps that even with more pressure on them, the home side probably weren’t going to score twice.
Khazri then had a free-kick palmed away by Fabianski straight into the path of Billy Jones who should have done better on the rebound, but sent his effort wide with the goal gaping.
Khazri himself should probably have been sent off for a deliberate stamp on Sigurdsson, but the referee deemed it only a yellow card offence.
Defoe’s first real chance of the day was deflected wide by Federico Fernandez after Khazri’s effort rebounded to him off Fabianski.
This may well be a result that the Swansea fans can look on and say that this is where they stayed in the Premier League for another year.
An astonishing achievement for Clement if Swansea do indeed stay up, as they were two points below their opponents today when he was first appointed.