Andre Gray pulled one back for the previously-unbeaten Hornets midway through the second period, and Nemanja Matic saw a red card in stoppage time but it was too late to provoke a dramatic twist from Watford.
The Red Devils had a chance within two minutes but Lukaku may have been caught cold, hesitating in getting a shot away and eventually being thwarted by Ben Foster as he tried to round the Watford goalkeeper.
Foster was alert again on 13 minutes when Paul Pogba let fly on his left foot from 25 yards out, getting his body behind the effort from the Frenchman who was allowed attacking freedom by Marouane Fellaini's holding presence.
David de Gea was soon called into action at the other end, diving low to his left to gather a Will Hughes shot which was lacking power, and then pushing a Troy Deeney strike over the crossbar after Watford had gone direct to their captain.
Alexis Sanchez's frustrations in a United shirt continued when he had a goal disallowed on 24 minutes. The Chilean chested down Pogba's cross and finished emphatically on the volley only to be flagged for offside.
Watford failed to react to that warning shot as the Red Devils moved through the gears with two goals in the space of three minutes.
Fellaini was in the thick of both the goals, making a nuisance of himself in the box for Lukaku's 35th-minute opener. Young recycled the ball and crossed for the Belgian to bundle the ball past Foster with his stomach.
Smalling's finish moments later was far more stylish as he controlled Fellaini's header on his chest before swivelling and volleying past Foster from eight yards out, the defender's fourth goal in his last 12 league games.
The visitors should have been out of sight before half time but Pogba cushioned his back-post volley straight at Foster.
Watford came out fighting in the second half in the hope of trumping their comeback against Tottenham Hotspur from a fortnight ago, but their offence was a little one-dimensional and Deeney's knockdowns were ultimately fruitless.
It took a slick passing move to break down United on 65 minutes as Abdoulaye Doucoure and Roberto Pereyra combined down the left flank to set up Gray for a thumping finish into the top corner from the penalty spot.
The visitors registered only one shot on goal in the second period and were content to sit back and try to hit Watford on the counter, but Javi Gracia did not have the options on the bench to break down Jose Mourinho's side.
Determined defending from Craig Cathcart and Christian Kabasele, who made last-ditch tackles to deny Sanchez and Anthony Martial respectively, kept Watford in the game right up until the death, and Matic's second booking for wiping out Hughes gave them a little bit more hope in the final minutes.
De Gea was needed to salvage United victory with a diving save from Kabasele's header as the Red Devils extended their run of winning games in which they score the first goal to 25 league matches.
Watford's own run is over but they remain in the top four despite a first home loss since April.
WATFORD (4-4-2): Foster; Janmaat (Femenia, 72'), Kabasele, Cathcart (Success, 88'), Holebas (Masina, 84'); Hughes, Doucoure, Capoue, Pererya; Deeney, Gray
MAN UTD (4-3-3): De Gea; Valencia (Bailly, 90'), Smalling, Lindelof, Young; Fellaini, Matic, Pogba; Lingard (Martial, 71'), Sanchez (McTominay, 84'), Lukaku