Anwar El Ghazi put Villa ahead after 11 minutes before Traore - signed from Lyon this summer - doubled the advantage with a delightful side-footed volley.
On Traore's debut, assistant coach John Terry said: "He hasn't played in a while. So to get the goal and top it off was good," Terry said.
"He was someone at Chelsea who was very hungry. He went away from the Premier League but he's always had that desire to come back and prove himself.
"He's got that opportunity now at Aston Villa and personally and professionally we're delighted to have him."