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The host needed just seven minutes to take the lead, Leon Bailey firing home, with Lucas Digne then dispatching a free-kick shortly after to leave Villa in control.
United pulled one back in the first half, Jacob Ramsey directing Luke Shaw's effort from distance into his own net, but he then scored at the right end shortly after the restart.
Erik ten Hag's side could not find a response, with Villa's defence never truly tested on what was another frustrating day for United.
Emery's return to the Premier League began in ideal fashion, Ramsey feeding a pass through to Bailey who showed his pace to find space away from Lisandro Martinez before sending his shot into the bottom-right corner.
The home side doubled its lead four minutes later as Lucas Digne expertly converted a free-kick from just outside the area to leave David de Gea with no chance and send Villa Park into pandemonium.
United reduced the deficit before the interval, Shaw letting loose from distance and the strike taking a wicked deflection off Ramsey.
Villa restored their two-goal lead three minutes into the second half, Ollie Watkins driving forward and laying off a pass to Ramsey, who arrived inside the box to fire a fierce effort into the roof of the net.
United failed to threaten a revival and suffered their fourth defeat of the season and first since the start of October.