United heads into the international break still second but now eight points behind leader Manchester City, which beat Arsenal 3-1.
United was outplayed by the technically superior Chelsea, which instantly recovered from a debilitating loss at Roma in the Champions League with a spirited performance that took the champions a point behind Mourinho's side in fourth place.
The goal was gifted in the 55th minute by the United defense, but it also owed much to Cesar Azpilicueta's vision and precision.
Morata peeled away from defender Eric Bailly and the striker was completely unmarked 12 yard (meters) from goal when he met Azpilicueta's pinpoint cross with a powerful looping header.
Morata was only signed by Chelsea in the offseason because Romelu Lukaku opted to sign for United rather than rejoining the Premier League champions from Everton. But while Lukaku has now gone a seventh game in all competitions without scoring, Morata's goal famine is over.