Rangers seemed set to hang on for a point before Santos headed over keeper Paul Jones and into his own net 11 minutes from the end.
Nygaard's goal - his ninth of the season - had put the home side ahead against the run of play.
Malky Mackay twice went close to scoring for Watford in the first half an hour. The defender headed Alhassan Bangura's free-kick over and then fired wide at the far post from Jordan Stewart's 29th-minute corner.
Another Stewart corner struck the outside of keeper Paul Jones' post as QPR struggled to get into the game.
The visitors suffered a setback when Clarke Carlisle limped off in the 38th minute.
Almost immediately, the Hornets conceded a penalty when Gareth Ainsworth picked out Lee Cook, who was brought down by Lloyd Doyley.
Nygaard sent goalkeeper Ben Foster the wrong way from the spot and was booked for tearing his shirt off in jubilation.
Worse almost followed for Watford when Furlong latched on to a long ball and lobbed Foster, but the ball bounced up onto the bar as the home fans were celebrating what they thought was a goal.
Less than a minute later, Watford equalised out of nothing. Foster's kick was flicked on by Darius Henderson and Ashley Young smashed the ball home from 25 yards.
Henderson then seemed fortunate to stay on the pitch after a challenge on Dan Shittu, the Rangers players were convinced there was the use of an elbow.
But it was the home side who found themselves down to ten men following the resulting melee.
Nygaard paid the price for angrily shoving Henderson, who was shown a yellow card for the foul on Shittu, while the R's striker was sent off for a second bookable offence.
Watford struggled to take advantage and substitute Theo Robinson headed Bangura's cross wide.
Ainsworth almost put QPR back in front with a volley that flew wide and Furlong went close with a header.
But Santos' moment of madness denied his team a draw and Rangers have now gone ten matches without a win under interim boss Gary Waddock.