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 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. Armenia won its first ever Chess Olympiad at the 37th Chess Olympiad. Sargissian played on board five for the Olympiad. The Armenia national chess team won gold ahead of China and the United States. Sargissian won the 38th Chess Olympiad in Dresden with the Armenia national Chess team, winning gold for the second time in a row at a Chess Olympiad. He played on board three and defeated Alexander Grischuk, the only win in a game with Russia, putting Armenia in the lead. Armenia ended up winning by one point ahead of Israel. Armenian President Serzh Sargsyan attended the Olympiad to support the team. After the Olympiad, they flew back to Armenia with him on the presidential plane, Air Force Armenia One. The Armenian national chess team won the World Team Chess Championship for the first time in 2011. Sargissian played on board four. Armenia and Sargissian regained their Olympiad title at the 40th Chess Olympiad. This was the third time Armenia won gold at the Olympiad. As the players were awarded their gold medals, the Armenian national anthemMer Hayrenik was played and the Armenian flag was raised in Istanbul. Levon Aronian was also holding an Armenian flag as he and his team were standing on the first place podium. Upon returning to Yerevan, the players were welcomed back with a ceremony by many people in the city the moment their airplane touched down in Zvartnots Airport. In 2014, Sargissian tied for 1st–2nd with Priyadharshan Kannappan in the 23rd Annual Chicago Open. In 2015 he tied for 1st–3rd with Pentala Harikrishna and Laurent Fressinet at the 2nd PokerStarsIsle of ManInternational Chess Tournament in Douglas, Isle of Man. In November 2017, Sargissian won the silver medal for individual performance on board 3 with a 2797 TPR, 6.5/9 score in the European Team Chess Championship. In December 2017, he shared 1st–3rd places with Hrant Melkumyan and Sebastien Maze in 9th CSC London Chess Classic FIDE Open. In February 2018, he participated in the Aeroflot Open. He finished eighth out of ninety-two, scoring 6/9.
Team competitions
Sargissian played for Armenia in the Chess Olympiads of 2000, 2002, 2004, 2006, 2008, 2010 and 2012. He took team bronze medal in 2002 and 2004 and team gold medal in 2006, 2008 and 2012. In the 2008 Chess Olympiad he won the gold medal for his individual performance on board three. He was a member of the gold-medal winning Armenian team at the World Team Chess Championship in Ningbo 2011. He also played for Armenia in the European Team Chess Championships of 2007, 2009, 2011, 2013 and 2015, winning team silver medal in 2007 and 2015, and individual gold in 2009. Sargissian played for "MIKA Yerevan" in the European Chess Club Cup in 2008, 2009, 2010, 2011 and played for "CA Linex Magic Mérida" in the 23rd European Chess Club Cup in Kemer 2007, winning team gold medal.
Awards
In June 2006 Sargissian was awarded the Movses Khorenatsi medal, in December 2009 the Medal For Services Contributed to the Motherland and in July 2012 the Order of Honor of the Republic of Armenia.
Chess school
In 2012, together with Levon Aronian, Sargissian founded a chess school in Yerevan, where the most talented chess players between the ages of 10 and 18 can study.