Thanks to some miserable Fulham defending, Villa raced into a 2-0 lead within 15 minutes, first netting through Jack Grealish at an angle from John McGinn's fine through ball (4), before Conor Hourihane slotted low from 12 yards from another McGinn assist (15).
Villa got a third just three minutes after the break as Tyrone Mings broke Fulham's offside trap from a Hourihane free-kick, poking home low, unmarked (48), while Fulham had a Bobby Reid goal disallowed by VAR after a foul by Aleksandar Mitrovic in the build-up.
Fulham have now lost all three opening Premier League games, conceding 10 goals, while Villa have won away in the Premier League for the first time since New Year's Day, upholding their 100 per cent record this season.
Fulham: Areola (5), Tete (4), Hector (5), Odoi (4), Ream (5), Bryan (5), Anguissa (5), Cairney (5), Decordova-Reid (5), Cavaleiro (6), Mitrovic (5)
Subs: Kamara (5), Le Marchand (4), Kebano (NA)
Aston Villa: Martinez (6), Cash (6), Konsa (7), Mings (8), Targett (6), Hourihane (7), Luiz (6), McGinn (8), Trezeguet (6), Watkins (7), Grealish (8).
Subs: Ramsey (NA), Traore (NA), Nakamba (NA)
Man of the match:John McGinn
How Fulham laid out red carpet for Villa
With speculation surrounding his future now settled, Grealish was outstanding in the first half, giving Villa an early lead as he latched onto McGinn's brilliant lofted ball over the defence. At the right of the box, Grealish's mind was made up by Fulham goalkeeper Areola, who dwelled on whether to come out, as the Villa man poked home from an angle.
Grealish was also involved in the second, darting into the box from the left after a one-two with Ollie Watkins, squaring for McGinn, and his neat lay-off was swept home by Hourihane into the bottom-right corner with his weaker right foot.
Villa were taking advantage of some woeful Fulham defending, enough for Sky Sports' Jamie Carragher to describe it as the worst in the Premier League this season, while Roy Keane said the Cottagers "were making Villa look like Bayern Munich".
Although Fulham had most of the ball (65 per cent), much of it was from wide areas - they made 36 crosses to Villa's two - as Mings and Ezri Konsa bossed the back line.
Their defending did not improve after the break as Fulham pushed up at a Hourihane free-kick, looking to catch Villa out, but Mings just stayed onside as he connected with the cross, stretching to touch past Areola for 3-0.
Fulham made three changes from the 4-3 defeat by Leeds - Tim Ream, Tom Cairney and Bobby Reid came in, replacing Aboubakar Kamara, Josh Onomah and Harrison Reed.
Villa were unchanged from the 1-0 win over Sheffield United, with new signing Bertrand Traore on the bench.
Areola then blocked McGinn's effort after he was put through on goal by Grealish, before Fulham looked to have got a lifeline as Reid capitalised on Emi Martinez's poor parry to turn home, only for VAR to spot a foul from Mitrovic on Konsa seconds beforehand.
Some last-ditch Villa defending assured their clean sheet; first Matty Cash cleared off the line from Andre-Frank Zambo Anguissa's effort, before Martinez superbly tipped Joe Bryan's left-footed shot onto the crossbar.
Although they had most of the play, the signs in defence and the lack of bite were worrying for Fulham - their owner Tony Khan apologised via Twitter seconds after full-time - while Villa simply took their chances as they look to avoid another relegation scrap.
'Tweet doesn't help doomed Fulham'
Sky Sports' Jamie Carragher on Monday Night Football.
"It was that bad a performance we were actually laughing at some of the defending. Fulham are going down, I've never been more certain of anything in my life, and they need to buy two, maybe three, four defenders.
"It never works [tweeting like Khan did] it always ends up in tears. What does Scott Parker think about that? What do those players in the dressing room, who may have to play next week at the back, think of that? Just keep your mouth shut.
"He was the one who was buying all those players two years ago, and made a mess of that. Shut your mouth, keep your head down, get on with it.
"It's difficult at Fulham at the moment, I'm more certain of Fulham going down than Liverpool winning the league. What we saw there defensively was unbelievable.
"Fulham were actually fortunate there was another game after them and we didn't properly analyse the goals.
"But Khan's tweet does not help. They were a mess last time they came up, what they don't want to be this year is a mess. They're going to go down, but almost go down as a club, be together, stick together."
What the manager said...
Fulham manager Scott Parker said: "I'm not too sure [how to sum up the game]. You dominate for large periods, you stream crosses into the box, we had a real control and endeavour about us. They enter our box on the first occasion, they score a goal. The second occasion, they score a goal.
"I've stood in this position for the first three games and it's a common theme of what I'm saying. You can't give up goals like we are, I've highlighted it and we know where we are.
"It's tough [to fix the defensive frailties]. I went with a back five today just to maybe give us a bit more solidity and it didn't work obviously. I felt like it worked well in possession but you just can't be that fragile.
"It's well documented that we are trying to bring people in, I've highlighted that and the club understand that.
"I feel like I can help the team, I think you saw that today. the way we set up and how we played and how progressive we were, I thought we looked like a very good team at times. But the decisions that are being made when the opposition are in possession and on that side of the game, it's tough."
Aston Villa boss Dean Smith: "We scored some quality goals. On top of all that, you have to find the balance in football, and that can be the desire to keep the ball out the back of the net, and the players have found that at the moment.
"This was always going to be a tough game for us, our first away game, and we knew they'd have the share of possession. But we knew with our quality and defensive ability we could get the win here.
"John McGinn being fit makes a massive difference. He's a fantastic player, and he was terrific tonight. Also Ollie Watkins, who will be frustrated not to get his first PL goal, but he's such an outlet for us, his work-rate and all the lads are patting him on the back for the role he's brought to our team."
- Aston Villa registered a clean sheet for the first time in their last 27 away Premier League games, since a 0-0 with West Brom in January 2016.
- Fulham have conceded 10 goals this season; only once has a team shipped more in their first three matches of a Premier League campaign (West Brom with 11 this season).
- Aston Villa have opened a Premier League campaign with back-to-back victories for just the third time, also doing so in 1995-96 and 1999-00.
- Aston Villa found themselves two ahead within 15 minutes in the Premier League for the first time since May 2011, when they led Arsenal 2-0 at the Emirates.
Villa now host Stoke in the Carabao Cup fourth round on Thursday at 7pm, before hosting Liverpool on Super Sunday, live on Sky Sports Premier League at 7.15pm.
Fulham go to rivals Brentford in the Carabao Cup on Thursday, live on Sky Sports Football at 5.30pm, before going to Wolves on Super Sunday, live on Sky Sports Premier League at 2pm.
Source: Sky Sports / Gerard Brand