New record signing Craig Beattie started up front and Lee Trundle was on the bench.
Mark Gower wasted a free-kick by hitting it straight at Hornets keeper Scott Loach after six minutes and the visitors went straight down the field to win a corner which was headed over by Adrian Mariappa.
Matty Collins then went close with a header from an accurate cross by Gower as the Swans pushed the visitors back.
In the 17th minute, Collins crossed into the middle where Gower spun to rocket a shot against the Watford crossbar with Loach beaten.
Midway through the half, Marvin Sordell blasted a shot that Dorus de Vries did well to punch clear and then Tom Cleverley fired straight at de Vries as the visitors went looking for the opening goal.
Both sides were playing neat football in the middle of the field but neither could find that final pass that would open up the opposition as the whistle blew for the interval.
Watford should have taken the lead straight from the kick-off but Sordell blocked a goalbound effort from a team-mate when the Swans defence was all at sea.
Nathan Ellington came on for the Hornets in the 53rd minute but a run down the middle by Beattie needed a superb tackle from Henri Lansbury to prevent the new signing from opening his account.
Ashley Williams followed Painter into the book and, from the resulting free-kick, Watford took the lead. Cleverley slipped a quick pass out to the unmarked Graham on the left and he fired low under de Vries and into the net in the 66th minute.
Trundle replaced Leon Britton in the 71st minute to the delight of the home fans but the visitors still looked more dangerous going forward although Painter went close with a header and Andrea Orlandi had a scorching shot turned round the post by Loach.
Swansea piled on the pressure in the closing minutes and, in stoppage time, skipper Tate powered a header into the top of the net from a Gower free-kick.