Sargissian won the Armenian Chess Championship in 2000 and 2003. He took part in the FIDE World Chess Championship 2004, but was eliminated in the first round by Sergei Tiviakov. Sargissian was victorious at Reykjavík 2006 and Dubai 2006. At the 8th Dubai Open in 2006, Sargissian scored 7/0 points, sharing first place with Sergey Fedorchuk and compatriot Tigran L. Petrosian. In 2007 he won the Ruy Lopez Festival (Zafra, Spain, March 16–25) finishing with 6.5/7, a point-and-a-half above the rest, including in particular players Ponomariov, Sasikiran, I. Sokolov. Sargissian won the Ruy Lopez Memorial 2007 in Zafra by an enormous 2½ point margin and with a 3021 performance rating. He came in third place at the 2008 Second Ruy López International in Mérida with 4.5/7 points. In 2009 he came first in the 18th Annual Chicago Open. He qualified for the Chess World Cup 2009 and was knocked out by Li Chao in the first round. Sargissian won the Annual Chicago Open 2012 with 7.0/9 points.