The Lions` play-off hopes were ended as goals either side of the break from Darren Pratley and Stephen Dobbie secured an impressive win for Swansea.
Brendan Rodgers` side can still draw level on points with second-placed Norwich - who play Portsmouth on Monday - as they ended an 81-year wait for a win in south London.
The visitors` fine start was rewarded when Pratley fired in a 30th-minute opener.
Dobbie robbed Jack Smith and slid in a cute pass inside to Pratley 30 yards from goal and the midfielder took one touch before smashing a powerful shot past David Forde and in off the post.
Swansea doubled their advantage two minutes into the second half when Dobbie weaved clear of a challenge before poking a finish high past Forde and into the roof of the net.
Source: PA
Source: PA