A simple web search doesn't seem to readily give the answer to this question. Who is the youngest player to defeat a reigning World Chess Champion in a classical chess game?
I'll start an answer just to get going as kmartin suggested. I'm sure it'll be superseded by other findings.
Carlsen beat Anand in Linares 2009 when he was 18 years and 3 month old.
If you don't mind including female chess players (I don't see any reason not to do so), I found that Maia Chiburdanidze, the seventh women's world chess champion, played a game in 1973 against the reigning champion Nona Gaprindashvili. The game was played in USSR Championship.
She was only 12 (born in 1961) and defeated Gaprindashvili.
Here is the link to the game: http://www.chessgames.com/perl/chessgame?gid=1285155
Maia Chiburdanidze took over the crown from Nona Gaprindashvili in 1978, aged 17.