The double took his tally for the season to 10, with the goals coming either side of Daniel Ayala being sent off for the visitors before the break.
The visitors had an early chance to take the lead when Andy Reid swung in a dangerous free-kick but Danny Collins glanced his header just wide.
Watford threatened soon after and Elliott Ward had to be alert to black Almen Abdi's goal-bound effort after the Swiss midfielder burst through the middle.
Billy Sharp spurned a glorious opportunity to hand Forest the advantage with 15 minutes gone. Chris Cohen found Simon Cox in space down the right and his low cross was turned wide by Sharp at the back post.
And they were made to pay when Guy Moussi conceded possession in the middle of the pitch. Abdi pounced to play in Vydra and the Czech made no mistake from inside the box.
Forest's task was made even harder when Ayala, who was booked earlier, picked up his second yellow in the 38th minute. The defender, on loan from Norwich, brought down Troy Deeney on the edge of the box and was given his marching orders.
The Hornets exploited their numerical advantage to great effect just before the break, with Abdi again laying on the assist for Vydra to finish from 12 yards.
Two half-time changes failed to stem the tide of Watford attacks and it should have been 3-0 after an hour when the ball fell kindly for Pudil on the edge of the box but he snatched at the shot and cleared the bar.
Forest, to their credit, showed some resistance after that but Watford were worthy of their lead and remained resolute in the closing stages.