Morgan, who completed his takeover of Wolves on Thursday, looked set to mark his first game in charge with a win after Nigerian international midfielder Seyi Olofinjana fired Mick McCarthy's side ahead in the 45th minute.
But battling Watford had not read the script and Jordan Stewart fired them back on level terms in the 87th minute before King struck from the spot in stoppage time.
Wolves substitute Jay Bothroyd then hit the post as Watford held on to get their bid to make an instant return to the Premiership off to the best possible start.
It was rough on Wolves who had controlled the game for long spells without taking advantage of their chances.
After a stuttering start, when Watford had gone close through Tamas Priskin, King and Tommy Smith, Wolves built up their own head of steam before Olofinjana made their pressure pay.
He was picked out by an excellent pass from Stephen Elliott, after Darren Ward and Andy Keogh had combined, and lifted the ball over goalkeeper Mart Poom.
Keogh and Stephen Ward then squandered chances to make the game safe and Wolves were made to pay the penalty.
Jobi McAnuff gave a sign of what was to come in the 68th minute when he was denied by Wayne Hennessey.
Darren Potter then gave away a free-kick three minutes from time that Stewart saw deflected past Hennessey.
Watford were revived and sensed the chance to pull off a smash and grab raid. They were effectively handed the three points by a clumsy lunge from Neill Collins on Lee Williamson.
The referee had no hesitation in pointing to he spot and King fired the ball into the roof of the net.