Ashley Williams scored the only goal to lift the Swans out of the relegation zone with victory over Waford at the Liberty.
New Head Coach Francesco Guidolin took in his first game watching from the stands, and the Italian would have been pleased with the performance.
Skipper Williams scored his first goal since March 2014 in what was the all important moment - the defender rising highest to nod home Ki Sung-Yueng's cross after 28 minutes.
This victory moved the Swans up to 17th on 22 points from 22 games.
The Swans made just one change to the starting XI.
Jack Cork returned to midfield in what was the only change to the side that was beaten by Sunderland last week. Kyle Naughton remained in the side after his ban was rescinded upon appeal.
Meanwhil, new Head Coach Francesco Guidolin took in his first game watching from the stands.
SWANS: Lukasz Fabianski, Kyle Naughton, Federico Fernandez, Ashley Williams (capt), Neil Taylor, Leon Britton, Jack Cork, Ki Sung-Yueng (Jordi Amat, 86), Gylfi Sigurdsson, Wayne Routledge (Modou Barrow, 65), Andre Ayew (Bafe Gomis, 81).
SUBS: Kristoffer Nordfeldt, Angel Rangel, Jefferson Montero, Marvin Emnes.
WATFORD: Heurelho Gomes, Allan Nyom (Juan Carlos Paredes, 74), Miguel Britos, Jurado, Valon Behrami (Obbi Oulare, 87), Troy Deeney (capt), Craig Cathcart, Nathan Ake, Ben Watson, Odion Ighalo, Etienne Capoue.
SUBS: Giedrius Arlauskis, Sebastian Prodl, Adlene Guedioura, Ikechi Anya, Almen Abdi.
The opening 20 minutes failed to create any real openings as both sides were defensively sound.
Some quick-thinking from Gylfi Sigurdsson sent Wayne Routledge through on goal following a fine backheel pass, but the winger was caught offside as he drilled straight at Heurelho Gomes.
Neil Taylor then bombed forward to create the next chance, which saw him tee up Jack Cork, but the midfielder skied his effort from 20 yards out.
At the other end, Odion Ighalo nodded well wide after skipper Troy Deeney had won possession off Taylor before crossing.
Then, on 28 minutes, came the opening goal.
After Gylfi Sigurdsson's delivery found its way to Ki Sung-Yueng, the South Korean's cross met Ashley Williams, with the Swans skipper holding off his marker before heading into the near corner.
The Swans were buoyed by their goal, and their link-up play was providing the visitors with problems.
Ki Sung-Yueng looked to double the lead when a cross was cleared into his path, but his left-footed effort failed to trouble Gomes as it flew high into the away end behind the goal.
Watford created a chance of their own just before the break as Jurado found himself in space, but his rifled effort was cleanly gathered by Lukasz Fabianski.
HALF-TIME: Swans 1 Watford 0
The second half saw a culmination of half-chances, with Jurado firing high and wide following a neat one-two with Deeney, before Miguel Britos headed onto the top of the net via a Ben Watson corner.
Watford came into the game a lot more, but the Swans kept plugging away and Cork fizzed a volley wide after Andre Ayew nodded down a Taylor cross.
The visitors, though, almost took advantage of a Swans mistake as a Leon Britton pass was intercepted and Jurado raced towards goal before curling a low effort just past the post.
The Swans made their first change with 25 minutes to go as Gambian Modou Barrow replaced Routledge, before Bafe Gomis came on for Ayew.
It was back and forth, and Jurado caught a clean connection with a volley that bounced in front of Fabianski, but the Polish keeper did well to collect.
The Swans made their final change in the last four minutes of normal time as defender Jordi Amat replaced Ki, which gave the hosts more cover at the back.
It was tense stuff at the Liberty, and the home crowd fell silent as a misplaced Taylor header was volleyed towards goal by Jurado, but his effort bounced inches wide.
Then, in injury time, the home side thought they had sealed victory when Gomis beat the offside trap before cutting back onto his left foot. His thunderous shot beat Gomes but not the woodwork as it cannoned back off the post.
The action continued, and the home crowd were again looking nervous as Deeney drilled a volley just wide of the top corner following Federico Fernandez's headed clearance.
But the Swans held on through three minutes of added time to claim a vital victory.