The Spaniard, whose 15 goals have been central to the Welsh club's successful fight against the drop, volleyed home an 86th-minute winner as Paul Clement's men came from behind to snatch the victory.
But Clement's side threatened to sign off their 2016-17 campaign with a defeat when Jonny Evans headed the opening goal of the game in the 33rd minute.
Swansea squandered numerous chances to level matters before Jordan Ayew's first goal for the club restored parity, and Llorente completed the turnaround four minutes from time.
Clement's brother Neil was part of the West Brom side that famously escaped relegation in their last match of the 2004-05 season, but Swansea's win at Sunderland ensured the older Clement sibling avoided any such final-day drama.
That victory over Portsmouth 12 years ago was West Brom's only win from 10 Premier League last-day fixtures heading into Sunday's match in south Wales, and it was the hosts who looked most lively early on at the Liberty, Leroy Fer blasting high and wide after a neat passing move sent him through on goal.
Kristoffer Nordfeldt – in for first-choice goalkeeper Lukasz Fabianski – got down well to keep out Salomon Rondon after 20 minutes, but he was culpable 13 minutes later as he ambled aimlessly under a hanging Darren Fletcher corner, allowing Evans to head home the opener.
16 - West Brom have now scored 16 goals from corners in the Premier League this term; the most of any team. Towering. pic.twitter.com/fTWDkUHMnE— OptaJoe (@OptaJoe) May 21, 2017
An unexpectedly fiery affair, tensions between Martin Olsson and Allan Nyom threatened to boil over shortly before half-time, the two full-backs going nose to nose following a touchline squabble.
Naughton then came close to adding to his goal at the Stadium of Light last time out with an effort that whistled just over.
Rondon outmuscled Federico Fernandez at the beginning of the second half to break clear on Nordfeldt but Leon Britton – so inspirational in Swansea's survival fight – tracked back to make a vital tackle in the box.
Fernandez then completely missed the ball when it sat up beautifully for him to head the home side level at the other end after 52 minutes, before penalty appeals at both ends were correctly ignored by referee Mike Dean.
Swansea's leveller finally arrived in the 72nd minute, when a Gylfi Sigurdsson free-kick was headed back across goal by Llorente for Ayew to head beyond Ben Foster.
And Llorente was on target to complete the comeback, volleying in from a Luciano Narsingh cross to get the party started in the stands.
GOOOALLL!!! 2-1!! LLORENTE!!! pic.twitter.com/cCOCM47Zjf— Swansea City AFC (@SwansOfficial) May 21, 2017