In 2004 Bruzon entered FIDE's top 100 by winning the B-group of the Corus Chess Tournament at Wijk aan Zee. He also became Cuban champion in 2004, and that fall he scored 8.5/11 on second board at the Calvia Olympiad, recording a 2771 performance rating.

Bruzon's steady rating gains continued into 2005, when he made an even score at the Corus Chess Tournament (2005) against an average opposition rated well over 2700. Other successes that year included a second consecutive Cuban Championship and the American Continental Championship (2005) at Buenos Aires 2005. First Ibero-American Champion at Ayamonte 2006 [brasilbase-1]. He won the Cuban Championship in 2009 also.
In 2011 Champion http://www.ajedrezenmadrid.com/torn... of the Americas Continental at Toluca, sharing 1st place with Mark Bluvshtein, Giovanni Vescovi and Yuniesky Quesada Perez. At the World Cup (2011), Bruzon defeated Yuniesky Quesada Perez, Francisco Vallejo-Pons and Le Quang Liem in the first three rounds, but lost to Ruslan Ponomariov during the blitz tiebreaker after drawing the classical games and both sets of rapid-play tiebreakers. His very successful participation (7.5/8 - +7 =1 against 6 GMs and 2 IMs*) in the Catalan team events in Spain launched him into the 2700 club for the first time. He competed in the 4th Ibero-American Championships held in Quito in Ecuador, winning his preliminary group and making the final, but came 3rd in the playoff for the top places. The Ecuadorian Chess Federation advised that it would not recognise the event for FIDE rating purposes, but it appears that it either changed its decision in this respect or FIDE took the matter into its own hands, and subsequently recognised the event in the October rating period. In July 2012, he played in the Quebec Invitational Open, and scored outright 2nd with 7/9, a half point behind Wesley So. He played second board for Cuba at the Chess Olympiad (2012) in Istanbul scoring close to par at 8/11 and finished 2012 by winning the 3rd JAHV McGregor tournament in Bogota, Colombia and the Internacional Copa AES 2012 held in the Dominican Republic.

Bruzon started 2013 by playing 2nd board for Cuba at the 9th Panamerican Team Chess Championship held in Brazil, the winner of which would qualify to play in the World Team Championships to be held later in 2013. Unfortunately for Cuba, while Bruzon scored a reasonably solid 4.5/6 (+3 =3), his country placed 2nd behind the USA.

Bruzon's rating as at 1 May 2013 was 2707, making him Cuba's second ranked player, the fourth ranked player in the Americas, behind Nakamura, Kamsky and Dominguez, and number 36 in the world. He does not have a rapid rating but in blitz his rating is 2755 (world #13).