Ki's ninth-minute strike, bundled home from close range, was enough to see off West Brom 1-0 and close the gap on Tony Pulis' struggling Albion side to two points.
It was certainly not pretty from a Swansea team still without a permanent manager since the sacking of Garry Monk over two weeks ago, but caretaker boss Alan Curtis has instilled plenty of fight and determination in his charges.
Albion forced them on the defensive for long periods, especially in the second half, but they could not find a way past a resilient Swansea rearguard in which Leon Britton and Ashley Williams were outstanding.
Both teams came into the contest low on confidence with Swansea bottom of the form table having failed to win in seven games and Albion equalling their worst run under Pulis - four matches without victory.
So it was no surprise that the football was a long way from the free-flowing variety with even the nature of Ki's ninth-minute summing up much of what was to come.
Swansea actually put together a neat attack with Wayne Routledge taking Andre Ayew's lay-off to play the ball into the path of Angel Rangel.
The Spanish full-back wasted no time firing against the post and the ball hit the back of Boaz Myhill, but the Albion goalkeeper fumbled as he tried to gather and Ki was on hand to tap home for his first goal since May.
Gylfi Sigurdsson soon shot straight at Myhill and it appeared as if Swansea's easy-on-the-eye style was coming back into their game.
But Swansea lost their way in what was to become an increasingly scrappy first period and West Brom, with skipper Darren Fletcher constantly probing from midfield, edged the balance of play.
The downside for Albion was that they created little in terms of scoring opportunities, although they did have genuine claims for a penalty when Rangel barged into Chris Brunt just inside the box after 28 minutes.
Brunt fired wide from distance with Lukasz Fabianski's handling only being tested at a succession of set-pieces, one of which left him requiring treatment after taking a bang in the ribs.
Swansea did manage to rediscover some fluency just before the break as Jefferson Montero saw his effort blocked by Jonas Olsson and Ayew, preferred in the main striking role to Bafetimbi Gomis, dragged his shot wide from 25 yards.
But Albion started the second period with purpose as James Morrison and Rickie Lambert brought saves from Fabianski, even if the Poland goalkeeper was not too unduly troubled, and the introductions of Saido Berahino and Stephane Sessegnon was another positive statement from the visitors.
Sessegnon set up a half-chance for Lambert which was squeezed past the near post as Albion piled on the pressure, Berahino seeing his shot blocked before Craig Dawson's header ended in the grateful arms of Fabianski.
But Swansea held on for only their second win in 14 games and their first at home since beating Manchester United at the end of August.
Source : PA
Source: PA