The Hornets took the lead through Andre Carrillo, the winger nodded home on the rebound after Lukasz Fabianski could only palm Richarlison’s shot up in the air.
Swansea got the equaliser through Jordan Ayew, as the forward managed to stay onside after Oliver McBurnie's knock-down to finish past the goalkeeper.
Substitute Luciano Narsingh sealed all three points as the game headed into the 90th minute, finishing past the goalkeeper on the rebound from Nathan Dyer's shot.
New shape under Carvalhal
Swansea lined up in a 4-4-2 shape, similar to what Carvalhal employed at Sheffield Wednesday. Renato Sanches operated on the left and Sam Clucas on the right flank, although the two did switch later on in the first half before Clucas moved into a central midfield role once Luciano Narsingh was subbed on at half time.
The Welsh side started brightly, Jordan Ayew struck the bar from 20 yards after winning the ball back in midfield, breezing past a challenge and firing an effort from distance that Heurelho Gomes could only watch fly past him.
After Sanches gave the ball away in midfield, Richarlison found himself on goal and stuck a shot with his left foot that went just wide as the forward attempted to impress his home fans after scoring just one goal at Vicarage Road all season.
Hornets sting first
A similar shot from Richarlison brought about the opening goal, as Carrillo was able to nod home from the rebound.
A long ball to Stefano Okaka found its way to the Brazilian wide man, but this time Fabianski could only palm his shot up in the air and the winger was first to the ball inside the box to head past the Polish goalkeeper.
Watford are a side that Swansea will look to emulate, after having a succession of different managers they appointed Marco Silva and brought a sense of identity to the club, with shrewd recruitment and faith in their manager, they have found success.
Appointing Carvalhal is a step in the right direction for the Swans, and a nod to their former ‘The Swansea Way’ ethos that brought the likes of Roberto Martinez, Brendan Rodgers and Michael Laudrup to the manager’s chair.
Despite the appointment, and chairman Huw Jenkins’ stunning interview on Friday, he hasn’t swayed many of the Swansea faithful with plenty of “We want Jenkins out” chants coming from the away end.
Second half continued in same vein
Despite the personnel change, Swansea started the second half very flat while Watford still posed enough of a threat through Richarlison – who caused Kyle Naughton all sorts of problems – as he showed a few minutes after the restart when he flashed the ball across goal to no avail.
Watford had the ball in the back of the net a few minutes later as Molle Wague headed home from a corner, but his effort was chalked off despite little contact being made in the box.
Swansea’s first chance of the second half came after an hour, Ayew couldn’t quite get the shot away and passed to Narsingh but the winger’s timid shot was blocked into Gomes’ hands.
This fixture has historically featured few goals - just six in the last five meetings - but neither side particularly created a lot until the Swans' late finish.
Substitute Andre Gray was put in on goal, in what was Watford's best chance of the game, but Fabianski was equal to the striker's effort, the save ended up keeping the away side in the game long enough to mount the comeback.
Late flurry rescues Swans
Swansea then scored twice in quick succession as Carvalhal got off to the dream start to life in South Wales.
Ayew equalised after finishing from McBurnie's knockdown, the Ghanaian thought he was the hero again after scoring the equaliser against Crystal Palace.
However it was Narsingh who would step up this week, finishing past Gomes from Dyer's long-range shot that prompted historic celebrations in the away end.
Carvalhal will not only be delighted with the much-needed three points, but the fact that his side came from a goal down and showed a response that had often been lacking this season.
The result leaves Swansea 19th in the table, but with plenty of optimism going into the new year after a momentous result.
While Watford sit comfortably in the top half of the league, making it two wins in a row after a poor run of six games without a win.