Palace used the wings well against the League leaders and looked risky on the attack, but their defence continued their shaky form and the return of Toure was completed when he was allowed to latch onto a low corner by Kevin de Bruyne to claim all three points.
Llorente, however, saved the day and the first three points for the former USA national and MetroStars head coach by striking twice in stoppage time to turn the tide. "After scoring my first goal, I was out of action for five weeks through injury".
Llorente had a slow start to the campaign and only opened his account in the Premier League in a 3-1 home defeat to Manchester City in September.
The Swans struck twice in stoppage time against Crystal Palace to pick up a three points to savour last weekend in one of the most entertaining Premier League matches of the year.
Nick Thompson here knew what was on the cards. We've got to be better than that. At least it seems to have added to man's popularity.
But just when you thought that was enough drama for one day, Swansea showed a fighting spirit that has been absent for most of the season so far and fought back magnificently.
Curtis said the wild scenes of celebration by staff and players following the final whistle had in many ways been for Bradley himself. If history has taught us anything, however, it is that this is not a race Pardew is expected to win. A 2-goal lead and we were pretty comfortable as Palace really weren't offering anything in front of Fabianski's goal. But I do see a benefit in having a major chat about those goals we conceded because we talked about it all week and I haven't had the response I wanted, if I'm honest, in terms of a couple of those set-plays, so I need to address that.
Bob Bradley celebrates at full-time after earning his first win as Swansea City manager. "I can not defend my defenders sadly enough, they need to do better than they have".
Bradley's side snatched victory from the jaws of defeat, scoring twice in a breathless stoppage time in a game which saw nine goals. Fernando Llorente - just off the bench in time for a corner at Bob Bradley's insistence - forces a block from Yohan Cabaye and the Dutchman puts in the follow-up.
"It has been a hard season and a lot of things have not bounced the right way". We need to enjoy this but it can't be something where we just take the good part without looking at it deeper because you won't win matches every day.