Mata converted from the spot after Anthony Martial sprinted down the centre of the pitch only to be brought down by Gareth McAuley, who was sent off for denying a clear goalscoring opportunity.
This match was a chance to welcome back Darren Fletcher, Jonny Evans and Anders Lindegaard to Old Trafford, all of whom had joined West Brom over the last 12 months.
The game was notable for seeing a rare Wayne Rooney substitution, who was replaced with 10 minutes left to play after another dispiriting performance in attack. There were audible ironic cheers when he was taken off by Louis van Gaal, and United's second goal came in his absence. Ander Herrera replaced him, the casualty for the introduction of Lingard as a first choice left winger.
These highlights, courtesy of NBC, can only be watched by those in the US