The Spanish striker was reportedly close to a move to Jose Mourinho's side before his eventual switch to the Blues and he haunted United with the game's decisive moment in the 55th minute.
The former Real Madrid man escaped the attentions of United's three central defenders – Eric Bailly, Chris Smalling and Phil Jones – to meet Cesar Azpilicueta's cross with an immaculate header and secure all three points for Antonio Conte's side.
United looked bright in the opening 20 minutes – coming close through Marcus Rashford's looping header – but faded badly and posed little threat during a desperately poor second-half display.
The defeat means they are now eight points behind Premier League leaders Manchester City, whose seemingly unstoppable march at the summit continued with a comprehensive 3-1 win over Arsenal earlier on Sunday.
Chelsea, who have now lost just once to United at Stamford Bridge in 16 league games, remain in fourth place, but are just a point behind their beaten opponents and Tottenham.
Conte responded to Tuesday's calamitous defensive display against Roma by replacing David Luiz with Andreas Christensen, while N'Golo Kante returned to the midfield after six games out with injury.
Chelsea had the ball in the net after just six minutes and might well feel aggrieved to have seen it disallowed. Marcos Alonso's cross was met in slapstick fashion by Jones, who skewed a volley past David de Gea, but referee Anthony Taylor ruled that Morata had pushed the England defender in the back.
United should have taken advantage of that reprieve just a minute later when Rashford escaped his marker to meet Ashley Young's cross. Fearing a challenge from Thibaut Courtois, though, the 20-year-old closed his eyes and his header looped harmlessly onto the roof of the net.
In a pulsating start to the game, Tiemoue Bakayoko then squandered a golden opportunity to give the hosts the lead. Davide Zappacosta's cross caused havoc in the United defence and fell invitingly for the former Monaco midfielder 12 yards out, but he could only horribly slice a half-volley over the crossbar.
Neither side could maintain the frenetic early pace and the next clear opening did not come until five minutes before the break. Cesc Fabregas' corner was met by the unmarked Christensen six yards out, but the Dane mistimed his jump and the ball bounced off his shoulder and over.
Chelsea's dominance in the latter stages of the first half continued into the second period, and they were soon rewarded as Morata scored his seventh league goal of the season.
Azpilicueta was given ample time to clip a cross towards the middle of the United area, where the Spanish striker sent a superb header into De Gea's top corner.
Mourinho responded by hauling off Henrikh Mkhitaryan and Jones for Marouane Fellaini and Anthony Martial, but it did little to quell the incessant wave of attacks by the hosts.
Bakayoko stole possession from the lumbering Fellaini but could only fire wide from the edge of the area, while the increasingly influential Eden Hazard saw a powerful drive parried away by De Gea.
United's best chances of a poor second half both came in the final five minutes. First, Rashford screwed a half-volley agonisingly past Courtois' post before the Belgian goalkeeper got down well to parry Fellaini's close-range effort.
An equaliser for United, though, would have been an unfair representation of a game that Chelsea dominated and thoroughly deserved to win.
Key Opta stats:
- Chelsea have lost just one of their last 16 Premier League home matches against Manchester United, winning 10 and drawing five.
- Jose Mourinho has seen his sides score just one goal in their last 10 away Premier League games against fellow 'big six' sides (D5 L5), with that strike coming at White Hart Lane in May.
- Alvaro Morata has had a hand in 10 goals in his opening 10 Premier League games for Chelsea (seven goals, three assists) – only Diego Costa was involved in more in his first 10 for the club (11).
- Cesar Azpilicueta has assisted Morata five times in the Premier League this season, more than any player has assisted another in 2017-18 so far.
- There are now eight points separating United in second and Manchester City in first – the biggest ever such gap after both the top two have played 11 games in Premier League history.