The visitors defended in numbers and took their opportunities in clinical fashion as Paul McGuinness' side failed to find a way past Villa's inspired keeper Craig Hill.
Clear-cut chances were at a premium in the first half although Andreas Pereira had an early shot blocked following a positive run by Sam Byrne. James Wilson dribbled past two defenders to work Hill and forced another stop out of the keeper before teeing up Byrne for a header wide.
As for Villa, Ben Pearson survived a challenge on Jack Grealish inside the area and Pierluigi Gollini made one routine save at his near post but things livened up after the break. Mats Daehli's intelligent lob was just too high after Hill came out of goal to head away a long ball by Pearson but the Midlanders then capitalised on a spell of pressure.
Courtney Wildin headed wastefully off target and Louis Rowley had to clear a Jordan Graham effort off the line. From the resulting corner, the Reds were outnumbered inside the six-yard box and Robinson plundered a simple finish when the ball was nodded back.
United's response was swift with Wilson deftly putting Byrne in the clear but the Irishman hesitated for a fraction of a second and Hill was off his line quickly to smother the danger. Wilson and Pereira made way for Jack Barmby and Jack Rudge with Barmby drilling a drive straight at Hill as Villa defended manfully.
A second goal on the break killed the match off as Grealish showed great tenacity to drive forward from midfield and play in Robinson, who cut