Martin Olsson's powerful effort brought Swansea level and, deep into added time, Llorente rose majestically to head in and prompt ecstatic celebrations at the Liberty Stadium. Victory moves the Swans five points clear of the relegation zone while Burnley, still without an away win in the league this season, slip to 12th in the table. The Clarets' tally of two points on the road is the lowest in the Premier League but, midway through the second half, they looked like ending their long wait for an away win. But ultimately justice was done as a dominant Swansea side recovered from the controversy of Gray's penalty to claim a deserved three points.
Until Llorente's dramatic winner, the game seemed destined to be defined by one of the most contentious refereeing decisions of the season. The introduction of video technology to assist referees has been the subject of intense debate for years, with the International Football Association Board discussing the matter as recently as Friday. If football's governing bodies were looking for evidence to support the implementation of video technology, Taylor's decision to award Burnley a penalty was a convincing argument. Vokes' arm was the only one outstretched in the Swansea penalty area from a Burnley corner and, despite the hosts' appeals for a free-kick for handball, Taylor pointed to the spot and Gray confidently converted.
The Swans' players, coaches and fans were as incredulous as they were furious and, energised by their raw sense of injustice, the home side took control of the encounter. They hit the woodwork three times in the first half alone - twice through Alfie Mawson and once through Llorente - but Burnley held on gamely and looked set to snatch an unlikely win when Gray swivelled and fired into the bottom corner in the second half. Despite boasting the joint-third best home record in the Premier League, a division-low tally on the road meant Burnley were far from immune to the threat of relegation.
In fact, their points-per-game ratio from away matches of 0.4 was the lowest of the Premier League era - but their fortuitously awarded first-half penalty suggested this might be the day their fortunes changed. It was not to be as Swansea, undeterred by falling behind, continued to dominate the encounter. They equalised as Olsson finished emphatically after Gylfi Sigurdsson's delightful backheel, and their relentless pursuit of a winner was eventually rewarded when Llorente towered above Burnley's defenders and planted his header firmly into the net. That gave Swansea a fifth win from eight games since they appointed Paul Clement, and the head coach summoned the spirit of a young Jose Mourinho as he celebrated Llorente's winner by sprinting along the touchline with his arms aloft, savouring the delirious celebrations of the home fans. Fer was the driving force in Swansea's midfield and Gray scored twice for Burnley, but Llorente's two excellent headers were the deciding moments of class - and could be the difference between survival and relegation for the Swans.