Andy Carroll poked home his sixth goal in six matches, and Mark Noble added two penalties to put the hosts 3-0 up.
The first spot-kick was awarded after Jose Holebas felled Diafra Sakho, and Almen Abdi brought down Michail Antonio for the second after the break.
Sebastian Prodl hooked one back for Watford and they also earned a late penalty, but Troy Deeney saw it saved.
And in the final minute of injury time, Hornets winger Nordin Amrabat was sent off for picking up his second yellow card.
The Hammers remain sixth in the Premier League, still three points behind fifth-placed Manchester United after their 2-0 win over Crystal Palace.
Liverpool also beat Everton 4-0 on Wednesday and are two points behind West Ham in seventh.
Watford remain 12th and will now focus on Sunday's FA Cup semi-final at Wembley against Palace.
Both sides have had their fill of penalty action this week.
Carroll scored one for the Hammers before they conceded a late spot-kick and equaliser against Leicester on Sunday.
And Watford earned a 1-0 victory over West Brom on Saturday - their first win in seven league games - largely thanks to Heurelho Gomes' two penalty saves.
However, Gomes was not able to save his side for a third and fourth time in 135 minutes of play.
Noble slotted both penalties home with ease, after Carroll had given the Hammers the lead by poking in from close range after a pinpoint ball from Dimitri Payet.
Watford got in on the action late on, when Angelo Ogbonna was adjudged to have brought down goalscorer Prodl in the area, but Deeney - on as a second-half substitute - was denied by Adrian.
West Ham came up against a much-changed Watford side, as manager Quique Sanchez Flores kept seven first-team players rested for Sunday's trip to Wembley.
And the Hammers dispensed of the Hornets with ease to earn a new club record.
Slaven Bilic's side have now gone 15 games without losing at home in the Premier League - their last defeat at Upton Park coming against Bournemouth on 22 August.
The record came in the third-from-final game at Upton Park ahead of the Hammers' move to the Olympic Stadium.
West Ham manager Slaven Bilic: "We can say they had half of their mind on the weekend and they rested players, but their line-up still had internationals.
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"We are victims of our success as the bar is always rising. We are coping with that well. This game was a big one because I told the players 'the season is good or very good anyway but after this game are we going to look up and try to catch those teams'. Still we have to look down as Liverpool are in good form."
Watford manager Quique Sanchez Flores: "The application was very good from us. We conceded really early and then it was very tough to play against a tough team like West Ham as they had confidence.
"In the second half, we reacted really well but not good enough to reduce three goals.
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"We have used a lot of players recently and the plan was to try to conserve and be fit for the weekend. Practically all of the players will be fit for the weekend."
West Ham travel to West Brom on Saturday, 30 April, while Watford make the short journey to Wembley for the FA Cup semi-final against Crystal Palace on Sunday.
Match ends, West Ham United 3, Watford 1.
Second Half ends, West Ham United 3, Watford 1.
Substitution, West Ham United. James Collins replaces Dimitri Payet.
Second yellow card to Nordin Amrabat (Watford) for a bad foul.
Foul by Nordin Amrabat (Watford).
Winston Reid (West Ham United) wins a free kick in the defensive half.
Corner,  Watford. Conceded by Adrián.
Penalty saved! Troy Deeney (Watford) fails to capitalise on this great opportunity,  right footed shot saved  in the bottom left corner.
Penalty Watford. Sebastian Prödl draws a foul in the penalty area.
Penalty conceded by Angelo Ogbonna (West Ham United) after a foul in the penalty area.
Corner,  Watford. Conceded by Adrián.
Attempt blocked. Manuel Lanzini (West Ham United) right footed shot from outside the box is blocked.
Foul by Valon Behrami (Watford).
Mark Noble (West Ham United) wins a free kick on the right wing.
Substitution, West Ham United. Emmanuel Emenike replaces Andy Carroll.
Nordin Amrabat (Watford) wins a free kick in the attacking half.
Foul by Victor Moses (West Ham United).
Attempt missed. Manuel Lanzini (West Ham United) right footed shot from the centre of the box is just a bit too high. Assisted by Michail Antonio with a through ball.
Attempt saved. Victor Moses (West Ham United) right footed shot from the centre of the box is saved in the bottom right corner. Assisted by Andy Carroll with a through ball.
Foul by José Holebas (Watford).
Victor Moses (West Ham United) wins a free kick on the right wing.
Juan Carlos Paredes (Watford) wins a free kick in the defensive half.
Foul by Andy Carroll (West Ham United).
Craig Cathcart (Watford) wins a free kick in the defensive half.
Foul by Andy Carroll (West Ham United).
Substitution, West Ham United. Victor Moses replaces Diafra Sakho.
Substitution, Watford. Troy Deeney replaces Almen Abdi.
Nordin Amrabat (Watford) is shown the yellow card for a bad foul.
Foul by Nordin Amrabat (Watford).
Cheikhou Kouyaté (West Ham United) wins a free kick in the defensive half.
Foul by Steven Berghuis (Watford).
Angelo Ogbonna (West Ham United) wins a free kick in the defensive half.
Mario Suárez (Watford) is shown the yellow card for a bad foul.
Foul by Mario Suárez (Watford).
Manuel Lanzini (West Ham United) wins a free kick on the right wing.
Foul by Steven Berghuis (Watford).
Angelo Ogbonna (West Ham United) wins a free kick in the defensive half.
Attempt missed. Steven Berghuis (Watford) left footed shot from outside the box is close, but misses to the right. Assisted by José Holebas following a fast break.
Attempt saved. Andy Carroll (West Ham United) header from the centre of the box is saved in the centre of the goal. Assisted by Dimitri Payet with a cross.
Corner,  West Ham United. Conceded by Juan Carlos Paredes.
West Ham beat Watford in a dramatic encounter at Upton Park to maintain their push for a place in Europe.