The Reds fell behind to Gabriele Angella’s double but Cox, Darius Henderson and Jamie Mackie came off the bench and scored in the order in which they were introduced to turn the game on its head, before Cox netted again late on.
Billy Davies’ side are now 10 games without defeat in the league, 12 matches in all competitions, and well positioned in the play-off places.
Troy Deeney curled a shot narrowly over the crossbar after three minutes following a neat exchanges of passes with Daniel Pudil on the edge of the penalty area.
At the other end Danny Collins’ diving header struck the bar after Guy Moussi had nodded an Andy Reid free-kick back across the six-yard box.
Watford did not clear the danger and Djamel Abdoun’s looping volley from the left side of the box dropped just wide of the far post.
Angella almost got on the end of a couple of corners. Both sides looked vulnerable from set-pieces but it would prove to be a warning that Forest did not heed.
Jamie Paterson forced Manuel Almunia into a save on the half-hour mark when he cut inside from the right flank on to his left foot.
It was third time lucky for Angella in the 33rd minute when his back-heel flick from Ikechi Anya’s corner put Watford in front.
Gonzalo Jara tried to keep it out on the far post but the Chilean could only head the ball against the underside of the bar and it bounced down over the goalline.
Another example of slack defending should have seen the unmarked Greg Halford equalise five minutes later but the defender, again given the nod to play as a striker by Reds boss Davies despite him having five recognised forwards sitting on the bench, sent a free header over the crossbar.
Deeney went close to extending Watford’s lead but his near-post volley from Anya’s cross went into the side-netting.
Davies replaced Halford with Cox at half-time.
Reid forced Almunia into a good parrying save shortly after the restart as Forest began the second half with some urgency.
However, Angella quickly knocked the wind out of their sails with a second goal.
Again it was poor defending as the Italian was given time and space to plant his header past Karl Darlow from Sean Murray’s inswinging free-kick.
Almunia helped Reid’s free-kick over the bar before Cox got the fightback moving in the 58th minute.
Abdoun’s inswinging cross from the left was headed back across goal by Moussi, and Cox swept the ball home from close range.
From then on it was all Forest and the inevitable equaliser arrived from a predictable source.
Former Hornet Henderson, on after 69 minutes, had been on the pitch less than five minutes when he stooped to head home Reid’s exquisite cross with the outside of his left foot.
Darlow got his fingertips to a Cristian Battocchio effort as Watford provided a reminder that they were still a threat.
However, three minutes later the comeback was completed.
Reid was involved again as he crossed for Mackie, fresh into the game, to head past Almunia from six yards out with 82 minutes on the clock.
Cox made absolutely sure of all three points when he slotted past Almunia in the final minute.