Sandro Tonali scored twice and Nick Woltemade added a third for the visitors, who came from behind after Villa keeper Marco Bizot was sent-off on the stroke of half-time.
In a match where VAR was not in use, Tammy Abraham had earlier put Villa ahead despite being in an offside position.
Bizot then saw red for taking out Jacob Murphy, allowing the Magpies to mount their second half fightback.
Analysis
This was a defeat for which Villa could have no complaints.
It was hard to escape the sense they gifted Newcastle a tie the officials - and to an extent their opponents - appeared trying to gift to them.
Villa got comfortably the better of the decisions. Had VAR been in use, their goal would not have stood, Lucas Digne might have been sent-off and would have certainly conceded a second half penalty for handball in the box.
Instead, despite those calls going their way, Villa were placed on the back foot by Bizot’s decision to hack down Murphy seconds before the break 40 yards from goal.
The keeper, admittedly, had been put in a nightmare position by Leon Bailey’s poor pass.
But it was still a rash decision and one which left his team a man down for the rest of the game.
There was an unmistakable irony about Abraham’s opener. Just under a fortnight after the striker had been denied a goal on his second debut for the club against Brentford by VAR, his goal here stood because of technology’s absence from this round of the competition.
Against the Bees, Abraham’s strike had been ruled out after video assistant Paul Tierney determined the ball had gone out of play 20 seconds earlier.
This time Abraham looked a good yard offside when Douglas Luiz chipped a central free-kick into the Newcastle box but the flag stayed down as he took a touch before finishing past Ramsdale. With no VAR, visiting protests were in vain.
Bailey sent a header wide, while Luiz fired over as Villa looked marginally the more threatening team.
Newcastle saw plenty of the ball but a Harvey Barnes effort into the side netting, after neat play by William Osula, was the closest they came to a leveller.
The visitors had further cause to be frustrated with the officials, however, when Digne slid in strongly to send Murphy flying. Referee Chris Kavanagh immediately showed a yellow card yet the slow motion replays used by VAR might well have upgraded to red had they been in operation.
There could be no arguments about Bizot’s dismissal on the stroke of half-time.
Villa were in the ascendency but when Bailey sent a poor pass toward the Newcastle box it set up the counter and Bizot, left in no-man’s land, brought down Murphy as he tried to round him.
With defenders racing back it was questionable whether the keeper needed to make the challenge but he could have few complaints with the result.
Most of stoppage time was taken up waiting for Martinez to put his shinpads on.
The Argentina international would be culpable for Newcastle’s leveller, after Villa should have the benefit of one of the worst refereeing decisions of the season.
Digne was a good yard, maybe two, inside the box, when Trippier’s free-kick struck his hand. Kavanagh and his assistant, incredibly, awarded a free-kick a yard outside the box.
Newcastle scored from it anyway. Martinez’s punch was poor and Tonali’s shot from the edge of the area deflected off Luiz to deceive the keeper.
The visitors brought on Anthony Gordon and he came a whisker away from putting them in front with a shot which deflected just wide.
But it was Tonali who was again on the mark to put them ahead. Bogarde’s defensive header only went as far as Dan Burn and he teed up Tonali to drill a shot into the bottom corner from 25 yards out.
With two minutes to go it was all over, Woltemade slotting home after Bogarde had lost the ball in his own box.
Key Moments
14 GOAL Tammy Abraham puts Villa ahead, finishing off a training ground free-kick routine despite a strong suggestion of offside.
45+1 RED CARD Villa keeper Marco Bizot is shown a straight red card for taking out Jacob Murphy 40 yards from goal.
63 GOAL Sandro Tonali levels for Newcastle, his shot deflecting off Douglas Luiz to beat Martinez.
76 GOAL Tonali puts the visitors in front, thumping a shot into the bottom corner from 25 yards out.
Teams
Villa (4-2-3-1): Bizot, Bogarde, Lindelof, Torres, Digne, Luiz, Onana, Bailey, Barkley (Buendia 65), Rogers, Abraham (Watkins 65) Subs not used: Konsa, Mings, Garcia, Sancho, Maatsen, Kone, Martinez (gk).
Newcastle (4-3-3); Ramsdale, Trippier, Thiaw, Burn, Hall, Murphy (Elanga 63), Tonali, Ramsey, Osula (Gordon 63), Woltemade, Barnes Subs not used: Willock, Murphy, Shahar, Neave, Park, Ruddy (gk), Pope (gk).