The Magpies had taken the lead three times through Genaro Snijders, Jon Stead and a stunner from Graham Burke against his former club, but a goal from Adama Traore and brace from Scott Sinclair ensured the tie finished level after 90 minutes.
Sinclair completed his hat-trick as the clock reached 100 minutes and Joe Bennett struck from the edge of the area to ensure that Notts' giantkilling exploits weren't extended beyond their 2-1 win at Huddersfield Town in round one.
There were two changes from the team that started Saturday's 1-1 draw with Accrington at Meadow Lane. Liam Noble dropped out of the squad, suspended following his red card against Stanley, whilst Thierry Audel had to settle for a place on the bench with Civard Sprockel recalled after recovering from injury.
McLeod, who signed for the club on Saturday, was handed his debut as a former County loanee, Jack Grealish, started for the Premier League side, along with summer signings Traore, Jordan Veretout and Jordan Ayew.
After an uneventful opening to the match, which was a misleading sign of what was to come, Notts stunned the famous footballing amphitheatre after a quarter of an hour by taking the lead.
Good pressing from the attackers saw the ball won high in the Villa half, allowing Snijders to take aim from 25 yards and his shot, with the aid of a deflection, looped past Bunn to send the travelling fans into pandemonium.
Roy Carroll smothered Kieran Richardson's cross before Sinclair could make contact and diverted the ball to safety, setting up a counter-attack which ended with McLeod turning Carlos Sanchez and rolling a shot wide of the upright.
The lead lasted just under 10 minutes as a trademark dazzling run from Grealish saw him mesmerise the Notts defenders, delaying his pass for long enough to find Traore in acres of space and the former Barcelona man smashed past Carroll from eight yards to level.
The home side looked to take control with Ayew and Traore both shooting at Carroll after slaloming past defenders. The Northern Ireland international was called into action again, saving from Sinclair with his feet after the striker had spun away from his marker.
Despite three divisions separating the sides, Notts remained a threat and reminded Tim Sherwood's side of that with Burke's curling effort from the edge of the area bringing a smart save from Bunn low down to his right.
McLeod's willingness to chase a seemingly lost cause earned the Magpies a penalty on the stroke of half-time as he was taken out in the penalty area by the goalkeeper, who was booked for the foul. Stead nervelessly placed the spot-kick into the top corner of the Holte End net, giving Moniz's men a narrow half-time lead.
Desperate to avoid an upset, Villa started the second half on the offensive with Traore drifting in from the right wing and flashing a shot into the side-netting.
They were level with their next chance as Grealish danced into the area and rolled the ball across the six-yard box to leave Sinclair with an easy tap-in on an open goal.
The turnaround was almost completed within a minute, Sinclair turned the ball over at the near post from Traore's deflected cross.
However, the next goal was to come from Notts and it was a stunner.
Burke cut in from the left after receiving a pass from Stan Aborah and unleashed a wicked, curling shot from 30 yards that kissed the post on the way into the net, leaving Bunn grasping at thin air. There was no muted celebration from the former Villa man as he savoured the moment in front of the Black and White army.
Aborah curled wide from 20 yards and Stead stung the palms of Bunn with a rasping drive before Snijders side-footed weakly at the goalkeeper from Burke's corner.
Grealish fired into Carroll's midriff and with just 13 minutes left on the clock the hosts were awarded a penalty when Richardson tumbled in the area. Sinclair squeezed the subsequent penalty past the goalkeeper to equalise for a third time.
Sinclair almost had a hat-trick but for a strong pair of hands by Carroll to send his near-post shot out for a corner and to hold a low effort minutes later.
Jimmy Spencer, back from injury much quicker than anticipated, placed a shot wide and Burke fired over the top with the last chance of normal time as the game ended 3-3.
Snijders shot into Bunn's gloves from 20 yards and Grealish saw an effort deflected wide as the end-to-end nature of the match continued into the extra half-hour.
Sinclair did get his hat-trick, side-footing past Carroll from substitute Joe Cole's cross to give Villa the lead for the first time on the night.
A golden chance came and went for County when Spencer shot wide after neat work by Stead. At the other end, the irrepressible Sinclair could have had a fifth - his fourth - but curled wide when one-on-one with Carroll.
Tim Sherwood's outfit did get their fifth goal when substitute Bennett was allowed to maraud forward and strike low into the corner from 20 yards to seal Villa's victory.
Grealish could have had the goal he so desperately craved, but spurned his chance when Carroll's clearance fell straight to him, curling wide of an unguarded net.
Carroll superbly denied Libor Kozak's powerful effort with a one-handed stop in the last action of a remarkable night of football.
Notts: Carroll; Hewitt, Sprockel, Swerts, Amevor (Audel, 71); Aborah, Burke; Snijders, Stead, Campbell (Jenner, 54); McLeod (Spencer, 82).
Subs not used: Loach, Hollis, Edwards, Valencic.