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.
Lions winger James Henry chanced his arm from long range inside the first minute before Swansea forward Dobbie saw his shot blocked at the other end after a trademark passing move.
The Swans were starting to dictate the play and Luke Moore had the first real chance in the 20th minute.
Nathan Dyer led a counter attack from inside his own half and after outpacing his defender slipped in Moore but the former Aston Villa man shot over the top.
Dyer got in behind again moments later when Angel Rangel played him in but his low, curling shot was well saved by David Forde.
The visitors momentum 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 Forde and in off the post.
Tamika Mkandawire saw his volley well saved by Dorus De Vries as the hosts looked for a response but the Swans doubled the lead just three minutes into the second period.
Rangel launched a long ball forward and Smith could only head the ball straight to the feet of Dobbie.
Dobbie weaved clear of a challenge before poking a finish high past Forde and into the roof of the net.
Millwall reacted well to the goal however and twice came close to a goal of their in their strongest spell of the afternoon.
Henry tackled Ashley Williams inside the area and sent in a shot which De Vries did well to keep out, and striker Steve Morison could only head the loose ball into the side-netting from close range.
De Vries then had to be agile to claw out a piledriver from Mkandawire from fully 25 yards before Henry sent another speculative effort over the top from way out.
Rodgers had the luxury of bringing on top scorer Scott Sinclair from the bench and the former Chelsea youngster twice came close to finding a third in the dying stages.
First he stung the palms of Forde from 20 yards and then he dragged a shot wide after running onto a flick.