Is the first game of World Chess Championship 2013 the shortest game in WCC history? The first game of the 2013 World Chess Championship, Carlsen vs. Anand, ended in a draw after just 16 moves. 

Is this shortest game in the history of the World Chess Championship?
There have been some shorter ones, for instance

Kasparov-Kramnik (2000), game 7, draw in 11 moves.

http://www.chessgames.com/perl/chessgame?gid=1252046

Kasparov-Anand (1995), game 18, draw in 12 moves.

http://www.chessgames.com/perl/chessgame?gid=1241980

Karpov-Kasparov (1984), game 29, draw in 13 moves.

http://www.chessgames.com/perl/chessgame?gid=1293014

The shortest games in WCC history I believe are the two 10 move draws at the end of the 1963 Botvinnik-Petrosian match, but it's clear Botvinnik had more or less given up the match before those games.

The shortest decisive game in a WCC match is reportedly Anand-Gelfand (2012), game 8, in which black resigned before his 17th move:

http://www.chessgames.com/perl/chessgame?gid=1666558