The Swans largely dominated the second half and on-loan Middlesbrough winger Emnes lashed home a low shot from 20 yards to settle the south Wales derby clash.
It was the Dutch player's second goal in four games for the Swans and left misfiring Cardiff, who sorely missed suspended striker Jay Bothroyd, licking their wounds.
Brendan Rodgers' men now lie just three points behind the Bluebirds and showed enough quality to suggest they can mount a sustained push for promotion this season.
They were vibrant throughout and in the seventh minute Swansea threatened when Emnes made the space to strike a fierce shot goalwards from 12 yards - but the effort was blocked by Mark Hudson.
An inswinging 16th-minute corner from the right flank by Peter Whittingham was met by a far-post header from Gabor Gyepes - but his 12-yard effort narrowly missed the target.
In the 19th minute, Swansea threatened when Nathan Dyer struck a fierce shot from 12 yards which drew a smart stop from Cardiff goalkeeper Tom Heaton.
Bothroyd, who is already into double figures in the scoring charts this season, picked up his fifth booking of the season in last weekend's 3-1 victory over Norwich, resulting in an automatic one-match ban for the target man.
On-loan striker Andy Keogh deputised for Bothroyd but it was Swansea who continued to look menacing as the lively Emnes headed over the crossbar in the 22nd minute.
In the 25th minute, Andrea Orlandi had a shot blocked by Cardiff defender Lee Naylor and moments later the same player went close again with a volley from 12 yards.
Orlandi was at it again in the 38th minute when he fired over from 25 yards before Craig Bellamy went close with a 12-yard shot that Dorus De Vries saved shortly before the break.
Whittingham tries his luck for Cardiff shortly after the restart but the momentum was soon with Swansea once more.
Angel Rangel had a shot well blocked by Gyepes and Scott Sinclair also went close.
Sinclair had a 66th-minute shot tipped around a post by Heaton from 12 yards out and then Hudson headed wide for Cardiff.
Bellamy also went close when he raced clear only for De Vries to make a superb save with his feet to deny the much-travelled striker.
There was a suspicion that Cardiff would be punished for Bellamy's miss and so it proved with 15 minutes remaining when Emnes collected possession and turned before striking a low left-foot shot into the bottom corner from 18 yards.
Bellamy went close with a header with two minutes remaining but the hosts could not find an equaliser, to leave Swansea toasting a famous victory.