The Turkish international, out of favour last season, made his first home appearance since last November and marked the occasion with a crucial opening goal at a time when Charlton were in full flow.
But he flawed his performance with a misunderstanding late in the game with goalkeeper Thomas Sorensen, which gifted an 86th minute goal to substitute Kevin Lisbie.
Villa sealed the points with a second goal in the 54th minute when JLloyd Samuel, like Alpay, opened his account for the club.
Villa pounded Charlton's defence before Lisbie's late effort and only a string of saves from Dean Kiely prevented further goals.
Injury-hit Villa were without both Olof Mellberg and Ronnie Johnsen and this allowed Alpay in to make his return and attempt to regain a permanent first-team spot.
Surprisingly, Charlton were the more positive in the early stages and Radostin Kishishev wasted a good opportunity when he blasted wide following a clever pass from Claus Jensen.
The Londoners were always quick on the break and Paolo Di Canio opened up Villa's defence with another astute pass, but on this occasion Shaun Bartlett's shot hit the bar.
In the 37th minute Villa took their shock lead, when a Lee Hendrie corner on the left to the far post was knocked back into the middle by Juan Pablo Angel, where Alpay powerfully scored on the volley.
It was a somewhat fortunate lead which they built upon when Samuel collected the ball on the edge of the area in the 54th minute and scored with a looping 20-yard shot.
David O'Leary, Villa's manager, was happy with the three points, but he admitted: "We were a little fortunate to be a goal up at half time, but we did take our chances."
Charlton's boss Allan Curbishley was not so pleased. He said: "We should have been in a commanding position by half time but came away with nothing."
Villa: Sorensen, Delaney, Alpay, Barry, De la Hendrie, McCann, Whittingham, Allback (Vassell 64), Angel. Subs Not Used: Dublin, Hitzlsperger, Postma, Stefan Moore.
Charlton: Kiely, Young, Fortune, Fish, Powell, Kishishev (Stuart 59), Parker, Holland, Jensen, Di Canio (Lisbie 82), Bartlett. Subs Not Used: Johansson, Royce, Perry.
Booked: Young, Fortune.
Attendance: 31,410
Referee: C Foy (Merseyside).