Midfielder Conor Hourihane made the main headlines with a hat-trick.
But teenagers Keinan Davis, who set up Hourihane's opener on his first EFL start, and Andre Green, who curled in a second for the hosts, both shone.
Josh Murphy and sub Nelson Oliveira each reduced the arrears after the break but, each time, Hourihane struck.
Villa's first four-goal haul since winning 4-0 at Sunderland in March 2015 was only their second league victory in nine matches, going back to last season, and the first time they have scored four at home since their 4-3 win over West Bromwich Albion in January 2014.
Hourihane's hat-trick was Villa's first in the league since Christian Benteke's three-goal haul against QPR in April 2015.
Meanwhile, Norwich are without a league win at Villa Park since a 3-2 win in November 1992.
Davis might have scored in the very first minute when he was thwarted by Norwich keeper Angus Gunn who then dived to save his powerful header. And, after setting up Hourihane's first goal, the teenager was this time denied when his cute lob came back off the bar.
There was even better to come for Steve Bruce's side just before the break when boyhood Villa fan Green, also just 19 years old, netted his first goal for the club with a superb right-foot curler.
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There could have been others too. Ahmed Elmohamady just failed to get on the end of Hourihane's cross, while James Chester should have done better with a close-range header at the start of the second half.
Those missed chances looked costly when Norwich pulled one back on the hour mark through the tricky, pacy Murphy.
Eight minutes later, Hourihane's hopeful right-foot 25-yard strike took a deflection before nestling in Gunn's top-left corner and, although the mood again became fraught when Oliveira scored just five minutes after coming off the bench, Hourihane had the final word.
Having been in the right place at the far post to drill home Davis's low right-wing cross for the first, this time he was a lot further out when he again found the top corner to complete the scoring five minutes from time. And there was still time to miss out on a fifth goal when Green was denied only by the bar.
Aston Villa manager Steve Bruce told BBC WM:
"We've had a difficult week, results-wise. But we were close to blowing Hull away in the first game and we were very close to blowing these away.
"It just shows you how quickly this club can lurch into a crisis, after a week. What has been going around is nonsense. I've got the nucleus of a decent team.
"We're young. And thankfully, under pressure, they've performed really well. We could have scored another four, if truth be known. And to get a hat-trick from a midfield player is terrific."
Norwich City manager Daniel Farke:
"The reason we lost was the first half. We made some silly and easy mistakes. We have to improve in the areas that we can influence.
"With having a third game in six days, we knew it would be a hard struggle but we didn't play well enough in the first half.
"We were very bad and Villa deserved to be in the lead at half-time.We knew they would be aggressive and motivated. It was almost a do-or-die game for them so early in the season."
Match ends, Aston Villa 4, Norwich City 2.
Second Half ends, Aston Villa 4, Norwich City 2.
Josh Murphy (Norwich City) wins a free kick in the attacking half.
Foul by Christopher Samba (Aston Villa).
Attempt saved. Andre Green (Aston Villa) header from very close range is saved in the bottom right corner.
Ahmed Elmohamady (Aston Villa) hits the bar with a right footed shot from the right side of the box. Assisted by James Bree.
Harrison Reed (Norwich City) wins a free kick in the defensive half.
Foul by Henri Lansbury (Aston Villa).
Foul by Marco Stiepermann (Norwich City).
Henri Lansbury (Aston Villa) wins a free kick on the right wing.
Attempt blocked. Conor Hourihane (Aston Villa) left footed shot from the centre of the box is blocked. Assisted by Ahmed Elmohamady.
Foul by Harrison Reed (Norwich City).
Glenn Whelan (Aston Villa) wins a free kick in the attacking half.
Substitution, Aston Villa. Christopher Samba replaces Keinan Davis.
Nélson Oliveira (Norwich City) is shown the yellow card.
Substitution, Norwich City. Yanic Wildschut replaces James Husband.
Goal!  Aston Villa 4, Norwich City 2. Conor Hourihane (Aston Villa) left footed shot from outside the box to the bottom right corner. Assisted by Ahmed Elmohamady.
Foul by Marco Stiepermann (Norwich City).
Conor Hourihane (Aston Villa) wins a free kick in the defensive half.
Corner,  Norwich City. Conceded by James Bree.
Nélson Oliveira (Norwich City) wins a free kick in the defensive half.
Foul by James Chester (Aston Villa).
Attempt blocked. Henri Lansbury (Aston Villa) right footed shot from outside the box is blocked.
Goal!  Aston Villa 3, Norwich City 2. Nélson Oliveira (Norwich City) right footed shot from the centre of the box to the bottom left corner. Assisted by Josh Murphy with a cross.
Marcel Franke (Norwich City) is shown the yellow card for a bad foul.
Foul by Marcel Franke (Norwich City).
Keinan Davis (Aston Villa) wins a free kick in the attacking half.
Attempt missed. Nélson Oliveira (Norwich City) right footed shot from outside the box is just a bit too high. Assisted by Marco Stiepermann.
Substitution, Norwich City. Nélson Oliveira replaces Cameron Jerome.
Substitution, Norwich City. Wes Hoolahan replaces Steven Naismith.
Attempt missed. Cameron Jerome (Norwich City) header from the centre of the box misses to the left. Assisted by Mario Vrancic with a cross following a corner.
Corner,  Norwich City. Conceded by Neil Taylor.
James Husband (Norwich City) wins a free kick on the left wing.
Foul by Ahmed Elmohamady (Aston Villa).
Christoph Zimmermann (Norwich City) wins a free kick in the defensive half.
Foul by Keinan Davis (Aston Villa).
Foul by James Husband (Norwich City).
Ahmed Elmohamady (Aston Villa) wins a free kick in the defensive half.
Attempt missed. Andre Green (Aston Villa) right footed shot from outside the box is close, but misses to the left.
Attempt blocked. Marco Stiepermann (Norwich City) left footed shot from the left side of the box is blocked. Assisted by Josh Murphy.
Aston Villa made light of their early-season wobbles as they deservedly beat Norwich City to claim their first Championship win of the season.