Cristiano Ronaldo's composed lob and Jadon Sancho's first ever goal for the Red Devils secured the victory in a match where David de Gea also came to their rescue.
The Spanish goalkeeper made a hat-trick of top class saves, denying Moi Gomez and Manu Trigueros in the first half.
The pick of the saves came after the break as De Gea got down brilliantly to deny Trigueros again - and this gave the away side the platform needed to get the three points.
Man United took the lead on 78 minutes when Ronaldo lobbed Geronimo Rulli after some slack play at the back from Villarreal.
And the victory was sealed in stoppage-time when Sancho rounded off a slick counter-attack with an emphatic finish in-off the bar to open his goalscoring account for the club.
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