Marcus Rashford cancelled out a first-half Etienne Capoue effort to leave the two teams on terms entering the final 30 minutes of the early kickoff, but late goals from Juan Zuniga and Troy Deeney, the latter of which came from the penalty spot, saw Watford beat Man United for the first time in 30 years.
Watford boss Walter Mazzarri made one change to the team that beat West Ham United last weekend and it came in defence as Younes Kaboul, who dropped out with a hamstring problem, was replaced by Sebastian Prodl.
As for Man United, Mourinho made five changes to the Europa League defeat to Feyenoord on Thursday night, with Antonio Valencia, Luke Shaw, Marouane Fellaini, Wayne Rooney and Zlatan Ibrahimovic all returning to the XI.
The first half-chance of the match fell to the visitors inside three minutes when Rooney, who was operating in central midfield, delivered a dangerous cross onto the head of Chris Smalling, whose flicked effort was just wide of the far post.
Watford settled after a difficult opening 10 minutes and had a chance to make the breakthrough when towering centre-back Prodl met a deep free kick at the far post, but his header just dropped wide of David de Gea's goal.
Three minutes later, Ighalo had a stunning chance to register when a mix-up between De Gea and Smalling presented the striker with an open goal, but he somehow fired wide of the post, much to the disbelief of the home supporters.
The pressure continued from Watford, and the home side had another opportunity in the 17th minute when Daryl Janmaat found the head of Deeney with a long-range cross, but De Gea flew across his goal to save.
Man United's best chance of the opening 22 minutes fell to Ibrahimovic after Rashford found the Swede with a low cross from the right, but the 34-year-old could only find the side-netting from a narrowing angle.
Paul Pogba then came close for the visitors after striking a powerful effort from the edge of the box, but the ball rattled against the crossbar as it somehow remained goalless after an end-to-end opening 30 minutes of action.
Watford eventually made the breakthrough in the 34th minute when Miguel Britos picked Martial's pocket in a wide position and Janmaat delivered a low cross in to Capoue, who found the back of the net with a well-placed shot.
There was some controversy over the opening goal, however, as Britos appeared to kick through Martial's leg to make the challenge and the Frenchman was replaced shortly after having not recovered from an earlier clash of heads with Janmaat.
Ibrahimovic came close to an equaliser in the latter stages of the first period when the Swede broke through on goal, but Prodl was on hand to make a last-ditch challenge and allow Watford to enter the half-time break with a one-goal lead.
Man United started the second half on the front foot and Ibrahimovic had a half-chance in the 47th minute after the ball fell for the striker outside the Watford box, but his effort was always moving wide of the post.
Man United were level in the 63rd minute, however, when Ibrahimovic delivered a telling cross into a dangerous position and it fell for Rashford, who slipped the ball through the goalkeeper's legs to equalise just past the hour mark.
It was the visitors that continued to press as the second period developed, with Juan Mata's introduction allowing Young to switch to right-back and free up Rooney in a central position behind the always-involved Ibrahimovic.
Watford threatened the Man United goal 20 minutes from time when a dangerous free kick was met by Prodl at the near post, but Shaw was on hand to clear the danger as the hosts continued to look threatening from set pieces.
Ibrahimovic fired a 25-yard free kick into the Watford wall in the 75th minute as Man United had another chance to score a second, before the Swedish striker had a header kept out by Heurelho Gomes as the pressure continued.
It was Watford that scored the game's third goal, however, as Roberto Pereyra found space in a wide position before setting up Zuniga, who found the back of the net less than one minute after coming off the bench.
The misery was not complete for Man United, though, as Fellaini brought Zuniga to the ground inside the box in stoppage time and Deeney was on hand to convert past De Gea as Mourinho's side lost their second league game of the season, following last week's home defeat to Manchester City.