Talisman Cristiano Ronaldo missed the clash due to a muscle problem, as Ralf Rangnick named five changes from the loss to Wolverhampton Wanderers in Victor Lindelof, Diogo Dalot, Fred, Bruno Fernandes and Marcus Rashford.
United set their intentions clear following eight minutes when Scott McTominay opened space in the area to head home Fred's pin-point delivery.
The energetic start continued in the matter of minutes this as Villa edgedcloser to the equaliser from a rasping attempt from close-range by Jacob Ramsey following a teasing delivery.
Villa preserved their bright spell seconds from the half-hour mark and saw the woodwork deny Ollie Watkins who managed to get a looping ball in-field and goal-sight.
Though, United regained momentum late in the half and were inches close to extend their lead through Luke Shaw, Rashford and McTominay amongst others.
Steven Gerrard's men levelled five minutes from halftime when Danny Ings knocked in a cutback, but it was chalked off after a review on the pitch-side monitor after a foul in the build-up.
The Clarets still fashioned in chances of their own inside the closing quarter with Matthew Cash's snap shot from outside the area forcing a smart save off goalkeeper David De Gea.
Dutch international Donny Van De Beek was thrown in the last 20 minutes by United, who withdrew Edinson Cavani seconds before goalkeeper Emiliano Martinez smothered Rashford's cross-cum shot.
Villa withheld United's pressure following the latter phases with moves of their own, which didn't unsettle the host who ran out victors for a fourth round ticket where they'll face Middlesbrough.