Unai Emery's side were four goals ahead at the break courtesy of efforts from John McGinn, Ollie Watkins, Leon Bailey and Youri Tielemans, before Alex Moreno added a fifth early in the second period.
Villa have moved back above Tottenham Hotspur into fourth, level on points with third-placed Arsenal and second-placed Manchester City, while Sheffield United remain bottom of the division, 10 points from the safety of 17th position.
The first half-chance of the match came for Villa in the fifth minute, with a short free kick being played into McGinn, but his powerful drive was always rising over the crossbar.
Sheffield United had a big opportunity in the ninth minute when Ben Brereton Diaz broke into the Villa penalty box before attempting to feed the ball under Emiliano Martinez, but the Villa goalkeeper managed to make the save.
Bailey then struck wide of the post down the other end after managing to work some space outside the Sheffield United penalty box.
Villa did make the breakthrough in the 12th minute, though, with McGinn having the simple task of firing into the back of the net from close range after Watkins's effort had come off the post.
Sheffield United defender Anel Ahmedhodzic was sliding in and almost cleared the danger, but the bounce off the post gave McGinn the opportunity to put his team ahead.
Villa then doubled their lead in the 16th minute, with Watkins racing onto a pass from Douglas Luiz before firing into the far corner of the net.
Two became three in the 20th minute, with Sheffield United carved wide open once again, and a brilliant team move ended with Bailey carefully placing the ball into the top corner after being allowed to dribble into the box.
Sheffield United goalkeeper Wes Foderingham did well to keep out Ezri Konsa in the 26th minute, before Tielemans had one headed off the line in the 29th minute.
Tielemans made no mistake from the resulting corner, though, with the Belgium international's thumping strike hitting the underside of the crossbar and dropping into the back of the net, which led to a number of Sheffield United fans deciding to leave the stadium.
Watkins looped one over the Sheffield United crossbar in the 33rd minute, and the two teams went down the tunnel at 4-0, with the Blades needing a minor miracle to turn the match around in the second period.
The Sheffield United fans would have been looking for an improvement at the start of the second half, but Villa had a fifth in the 47th minute through Moreno, who fired a Watkins cross into the back of the net.
Jayden Bogle lifted one just past the Villa goal in the 51st minute, with ironic cheers arriving from the home supporters, as their side finally had a positive moment in the final third.
Villa were cruising, with the players clearly conserving energy for the games ahead, and Sheffield United were finding it so difficult to carve out anything of note.
Foderingham made a smart save to deny Moussa Diaby in the 72nd minute, before Sheffield United had a couple of golden chances to score in the 77th minute, with Martinez making smart saves to deny Gustavo Hamer and Jack Robinson after pin-ball inside the box.
Debutant Morgan Rogers swept one over for Villa late on, before Sheffield United's Vinicius Souza saw a late goal disallowed for offside, which summed up a difficult evening for the hosts.
Villa will now switch their attention to the FA Cup, preparing to welcome Chelsea for a fourth-round replay on Wednesday night, before hosting Manchester United in the Premier League next Sunday.
Sheffield United, meanwhile, will look to bounce back from the heavy defeat when they travel to Luton Town next Saturday.