Andre Gray opened his account for the club after just 13 minutes to give them the lead, but Tammy Abraham's equaliser 11 minutes into the second half looked to have earned a second consecutive draw for the Swans.
However, Richarlison rescued all three points for Marco Silva's side in the final minute of normal time to see them return to winning ways following last weekend's 6-0 home drubbing at the hands of Manchester City.
Swansea only had themselves to blame for the opening goal early on as two errors contributed to Gray's first goal in a Watford shirt, the second of which saw the defender steer the ball straight into his path to leave him with a simple finish from close range.
Gray had the ball in the back of the net once again on the half-hour mark, but this time his celebrations were cut short by the offside flag.
The hosts were level in the 56th minute when Abraham showed his predatory instincts in the area, reacting quickest after Heurelho Gomes had denied Wilfried Bony's initial effort to sweep the rebound home from close range.
It was ultimately defensive mishaps which cost Swansea a point, though, as Richarlison pounced onto a loose pass inside the hosts' half late on before coasting past a weak challenge and firing his finish in off the underside of the crossbar.
The result sees Swansea drop a place to 14th in the Premier League table with just one win from their opening six games, whereas Watford sit level on points with Tottenham Hotspur and are only outside the top four on goal difference.