The former Ipswich striker had already spurned two good chances when he headed the winner at Vicarage Road as Paulo Sousa’s side strengthened their hold on a play-off place.
However the visitors were indebted to a pair of goal-line clearances from skipper Alan Tate as they shut out Watford – who are now right in the thick of a battle against relegation.
Malky Mackay’s side find themselves just two points above the relegation zone in a congested table and will need to make the most of the visit of doomed Peterborough on Saturday to stave off the threat of the drop into League One.
Kuqi capped a frenetic first 45 minutes in which both sides should have scored at least twice with the solitary goal as the Swans made it an incredible 23 goals conceded in 35 league games.
John Eustace had the first shot of the night but hit the roof of the stand behind the goal from 25 yards before Danny Graham saw a header cleared from off the line by Tate as Watford made a lively start.
Centre-half Martin Taylor saw a shot blocked from a deep free-kick before Craig Beattie came close to giving the Swans the lead in their first attack.
Darren Pratley flicked on a long pass and after shrugging off the attentions of Adrian Mariappa, Beattie drilled in a powerful effort which Watford’s highly-rated goalkeeper Scott Loach did well to beat out at the near post.
That chance sparked Swansea into the life and Pratley then crossed for Kuqi to climb above Loach but the Finn saw his weak header crash against the base of the post.
Kuqi again should have done better minutes later when he headed an excellent cross from Cedric van der Gun straight at Loach, but did finally score at the third time of asking in the 18th minute.
Angel Rangel cut out a pass by Watford midfielder Henri Lansbury and started a lightning-quick counter attack.
Pratley found Beattie in space on the right and his fine early ball found Kuqi inside the six-yard box.
England Under-21 keeper Loach got a strong hand to his diving header but the ball found its way into the net.
Only an agile save from Dorus De Vries prevented Jon Harley from heading the home side level as the home side made a bright response and Tate made his second crucial clearance from under his own crossbar to volley Jay DeMerit’s header clear before half-time.
The opening of the second period failed to live up to the first as both sides struggled to control the ball on a difficult surface.
DeMerit headed over from a long throw as the home side attempted to exert some pressure while the Swans were content to rely on their extraordinary defensive record to see out the win.
And De Vries was able to record another clean sheet after keeping out a late effort from Heidar Helguson as Sousa celebrated three more points.