While the first leg was competitive without producing any goals, it was one-way traffic on Thursday night as Ollie Watkins, Leon Bailey, Jhon Duran and Moussa Diaby all got on the scoresheet.
The low point of the night was Watkins suffering a knee injury that led to his early withdrawal, while Diego Carlos also needed to be substituted later in the contest, but Unai Emery will be delighted with such a dominant performance over the fallen Dutch giants.
In response to Ezri Konsa being suspended and the 4-0 defeat to Tottenham Hotspur on Sunday, Emery made four changes, including bringing each of Morgan Rogers and Diaby into his starting lineup.
Rogers's only contribution during the opening 11 minutes was to pick up a caution for a late challenge, yet it was the most eventful moment during a low-key start.
Ajax midfielder Sivert Mannsverk and Villa forward Ollie Watkins followed Rogers into the book as the referee attempted to stamp his authority on the game.
The first shot of any note finally arrived in the 22nd minute, a neat Villa move ending with Bailey firing a low shot wide of the far post from 15 yards out.
Diaby frustrated his teammates by failing to make the most of an opportunity when rounding goalkeeper Diant Ramaj, but from the resulting corner, Villa went ahead through a brilliantly-taken header from Watkins who arrowed his effort into the far corner.
However, Watkins was forced to depart soon afterwards, a consequence of the knee injury that he sustained in the earlier challenge that earned him a yellow card.
Not long afterwards, Ajax had to make their own alteration as Ahmetcan Kaplan suffered a dead leg, leading to an attacking change with Chuba Akpom being introduced in attack and Ajax reverting to a back four.
That only allowed Villa to have more possession and after a sustained period with the ball, the home side went close to a second with Rogers curling over from 20 yards.
Ajax had created next to nothing throughout the first half, yet in the closing seconds of five minutes of added-on time, Matty Cash was forced to clear a goalbound effort from Brian Brobbey off the line after the forward had met a cutback.
The start of the second half was as uneventful as the first, which suited Villa, until Duran failed to convert a half-chance when meeting a cross from the left, Ramaj doing enough to put off the Colombia international.
Within a minute, though, the home side were two goals ahead. From the resulting goal kick, Ajax tried - and failed - to play out, and after the ball arrived at the feet of Bailey, a neat bit of skill freed up the space for him to coolly slot into the bottom corner from 10 yards.
Villa had their tails up and Duran should have probably converted a header from six yards out after meeting a corner, before driving at the Ajax defence and slicing an effort wide.
Things went from bad to worse for Ajax when Mannsverk was sent off for receiving a second yellow card, the midfielder unable to have any complaints after cynically pulling the shirt of Duran.
On his first appearance since January 14, Duran was putting together one of his best performances in a Villa shirt, and he got the reward that his showing deserved with his third goal of the season.
The ball fell invitingly to him on the edge of the area after a Ajax defender had failed to deal with the danger, Duran taking advantage by firing an unstoppable shot in off the underside of the crossbar.
As the clock ticked into the final 10 minutes, Villa added a fourth through Diaby, who was left with acres of space down the right before drilling the ball inside the near post after cruising into the penalty area.
Villa were able to see out the closing minutes with minimal fuss, the referee also choosing to play no added-on time, and Emery and his squad can now look forward to Friday's last-eight draw.