The result left Villa second on 12 points with a game in hand over leaders Everton who have 13. Third-placed Liverpool have 10 from five and Leicester in fourth are on nine after suffering their second successive home defeat.
Barkley, who is on loan at Villa from Chelsea, snatched the winner out of the blue at the King Power stadium with a stinging low shot from 25 metres which left Leicester goalkeeper Kasper Schmeichel clutching thin air, as the ball bounced in front of him.
The England midfielder, who also scored on his Villa debut in a 7-2 home drubbing of Liverpool in the previous round of matches, was delighted as they started the season with four wins for the first time since 1930.
"An important win today as they were on top and we started slow but we improved and in the end deserved it," he told Sky Sports.
"I was 50/50 in the week and (our physio) did a really good job getting me right. He said I would end up scoring the goal and I did so I dedicated the goal to him.
"The manager has given me the platform to play and I am excited and looking forward to every game."
A drab first half produced one chance at each end, with Villa keeper Emiliano Martinez denying Leicester right back Timothy Castagne before Egyptian forward Trezeguet fired wide after a flowing move by the visitors.
Villa, who were on the back foot in the opening half, came forward with more purpose after the beak and went close in the 51st minute when central defender Ezri Konsa headed inches wide.
When the match appeared to be heading for a goalless stalemate, Barkley stepped up to make sure Villa stayed the only Premier League team with a perfect record this season after they narrowly avoided relegation last term.
"We have seen Ross Barkley do that enough times for Everton and Chelsea so we are pleased he did it for us today," Smith told the BBC.
"It was touch and go whether he started today. He had a knock to the knee but a great goal and a real battling performance by the whole team.
"We are just looking at the next game. We will savour what we are doing at the moment and look forward to the Leeds game."
--Reuters--
