Note this is different in to the Chess Player to lose in the least moves in that here, the Player either resigns or defaults. It is debated whether these are actually 'games' since a single move is not completed. Anyway...
Fischer-Spassky (Reykjavic, 1972). Game 2
1. forfeits
Bobby Fischer versus Oscar Panno on Dec. 12, 1970.
1. c4 resigns
Panno was upset that Fischer (and also Reshevsky) were to have their last round games begin at a different time than all the others (due to religious beliefs.) The tournament book indicates Fischer took 10 minutes before playing 1.c4, and Panno waited some 52 minutes before returning to the playing site and resigning. (Note that he did RESIGN--this is in fact different from Spassky-Fischer, game 2, where Bobby FORFEITED.) Also note that the Panno game was the first one where Bobby played 1.c4. Versus Polugaevsky in round 11, he played 1.c4 Nf6 2.g3 c6 3.Bg2 d5 4.Nf3 Bf5 & 1/2, 38.
It has been said that Panno didn't actually return to the playing site, and resigned without being there.
Source
rec.games.chess.misc
Date: Jun 1997