Chelsea led early on through Didier Drogba but headers by Richard Dunne and James Collins turned it round and continued Villa's good early season form.
"We know we are a good side, we have confidence and the last performance here (against Manchester City) was really good," Dunne told Sky Sports.
It did not look so good for the hosts after 15 minutes when Chelsea, who bounced back from defeat at Wigan Athletic with an impressive win over Liverpool, took the lead when Brad Friedel misjudged a bouncing Drogba shot from the edge of the box.
Villa, who had lost at home to Chelsea only once in the last 10 years, kept their composure and levelled when an Ashley Young corner skidded off the head of Frank Lampard and allowed Dunne to fling himself forward and head home.
Even worse defending early in the second half allowed unmarked defender Collins to head the second from another Young corner - the former West Ham United defender's first goal for more than three years.
Chelsea had chances to equalise but Friedel made up for his early blunder with some solid saves.
"We can definitely compete, we've got a lot of good players in the squad and it was a great effort against a top quality team," said Villa boss Martin O'Neill.
"My own view is that anybody who finishes in front of Chelsea will win the Championship."
Ancelotti said: "We lost because on two set plays Villa scored. We need to focus more on these situations.
"I thought we played a good game but we don't want to lose a game through these situations, only if the other team played better than us."
