Cox was making only his second league start since his £2million summer switch from Swindon and made the most of his rare chance to grab his first league goal for the club.
His 68th minute strike, Albion's fifth, set the seal on a stunning success as Roberto Di Matteo's side roared back to form.
Albion had taken just five points from their previous six games and failed to score in their last two matches.
But early first-half goals from Jonas Olsson and Graham Dorrans put them in control before Luke Moore, Gianni Zuiverloon and Cox struck after the interval as Watford's impressive away record came to a shuddering halt.
Watford had arrived at The Hawthorns unbeaten on the road in the Championship for six games.
But that good form was undone by some poor defending as Watford again left Albion empty handed with their last win at The Hawthorns coming back in 1995.
Having conceded the first goal in their previous five home games, Albion went some way towards redressing the balance through Olsson's fifth minute strike.
The Swedish central defender cashed in with a far post header following a left-wing free-kick from Dorrans that Watford had conceded after a rash challenge on Joe Mattock by Lee Hodson.
That strike effectively opened the floodgates for Albion who quickly doubled their advantage when Dorrans struck in the 18th minute from the spot after Watford captain Adrian Mariappa sent Moore sprawling.
Albion thought they had earned a second penalty in the 33rd minute when Moore went down under the challenge of Hodson.
This time Miller viewed it as a dive by Moore and booked the former Aston Villa striker. Moore was fuming but did not have to wait long to make up for that disappointment.
Just seconds after Danny Graham had missed a 48th minute sitter at the far post which would have given Watford a lifeline, Moore made the game safe when his persistence paid off.
After a powerful run unto the area, Moore saw his first effort saved by Loach before latching on to the rebound and curling home his shot from 16 yards.
Zuiverloon got in on the goalscoring act in the 63rd minute by cutting in from the right-wing and letting fly with a fierce angle drive that whistled past the helpless Loach.
Cox then struck five minutes later. Good work by Moore saw the ball break free to Cox and he beat Loach with a powerful rising drive from 20 yards.