Ivanov has celebrated success in various chess tournaments. He won the 1994 Russian Championship, came second in a 1995 tournament held in Szombathely, Hungary, and secured third place in the 1998 championship tournament in Ubeda, Spain. In 2002, Ivanov won the Cup of Russia in Moscow and was the runner-up in the Russian Championship. In the following year, he also achieved victory in the Nikolaev Anatoly Memorial Tournament and came second in the Russian Superfinal Championship and the 57th Championship in Russia.
In 2004, Ivanov won the Cup of Russia for the second time and ranked third in the 57th Championship in Russia. Later, he won the 2005 Russian Championship Superfinal but came second in the 58th Championship in Russia that year.
Ivanov also played in team competitions. He contributed to the bronze medal victories of Moscow at the Green Marathon Cup, a rapid tournament in Serbia, in both 2005 and 2006.
Ivanov's playing style is characterized by a good sense of the initiative and a profound understanding of the chessboard. He is best known for tactical acuity and opening knowledge, particularly in the Sicilian Defence, French Defence, and Caro-Kann Defence. His personal contribution to chess theory, especially in the various system of the Sicilian Defence, is highly esteemed in the chess world. He is especially known for his ability to surprise opponents with unexpected moves.