England international Barkley, 20, who injured himself just before the start of the season, provided a welcome boost for Roberto Martinez's side who until Saturday had struggled to live up to the standards of last season when they finished fifth.
Barkley's return is good news for both Everton and England with another Euro 2016 qualifying match next month.
"On Thursday, Ross put the ball in the top corner three times out of nothing in a training exercise," Martinez told reporters. "I think that was his way of letting everyone know that he was ready.
"Even when he came off, he looked quite fresh and I think he wanted to play even longer.
"Usually in a footballer you have an outstanding technical ability or an exceptional physical ability, but Ross has got both."
Goals from Phil Jagielka, Romelu Lukaku and Seamus Coleman hoisted Everton up to 12th in the standings while Villa have now lost four league games in succession.
"Today was a really strong team performance, which is pleasing when you come back from the international break," Martinez added. "We had to be patient with Ross.
"I didn't expect him to last as long as he did, but he got the tempo of the match very quickly. It's good to see him back."
Villa boss Paul Lambert was disappointed with his side's display.
"We got what we deserved," he said. "We lost poor goals at bad times of the game. We spoke about not switching off against Everton. They finished in the top five last year. We had to be better and we take our medicine."
(Reporting by Martyn Herman; editing by Toby Davis)
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