By Guido Guidi/Getty Images The first goal in the extra-half saw a young Gianluigi Buffon volley into the bottom corner, leaving the home fans and the hosts disheartened.
It was the first goal of the game for the Juventus striker, but the home side had the better of the chances.
Gianlui Buffon opened the scoring after 25 minutes with a header, but Wales keeper Ben Smith was quick to equalise with a shot from outside the area.
Alves opened the second half with a goal, firing his effort into the top corner, before another shot from close range was blocked.
The game was restarted just before the break, when Wales substitute Martin Olsson was sent off.
The win moves Juventus to the top of the Serie A table, five points ahead of Roma.
Wales have been in the Europa League play-offs, having been eliminated by Inter Milan in the group stages last month.