Arnau Ortiz gave Atletico an early lead when his cross-shot found the far corner, but the English team responded strongly and dominated much of the first half.
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Mbeumo levelled from the penalty spot after Shea Lacey was fouled before completing the comeback after Jack Fletcher won possession high on the right.
United also impressed defensively, with Leny Yoro excelling at right-back and keeping Ademola Lookman quiet.
Mason Mount was outstanding in a deeper midfield role, while Andrey Santos again delivered a composed display.
The performance offered manager Michael Carrick plenty of encouragement ahead of the new campaign.