Kazhgaleyev played for Kazakhstan in the Chess Olympiads of 1996, 1998, 2000 and 2008. In 2004, he tied for first with Slim Belkhodja in the 27th Syre Memorial in Issy les Moulineaux. Kazhgaleyev competed in the Chess World Cup 2005: he knocked out Evgeny Alekseev in the first round to reach round two, losing to Teimour Radjabov and thus exiting the competition.
In 2007 he tied for 3rd–9th with Dmitry Svetushkin, Vladimir Malakhov, Evgeny Vorobiov, Pavel Smirnov, Vladimir Dobrov and Aleksej Aleksandrov in the 3rd Moscow Open tournament.
In 2011 he tied for 2nd–5th with Parimarjan Negi, Csaba Balogh and Jon Ludvig Hammer in the 13th Dubai Open Chess Championship. Later that year Kazhgaleyev took part in the Chess World Cup 2011, where he was eliminated in round one by Dmitry Andreikin.
In January 2015 he came second to Ni Hua in the Australian Open. Bin-Sattar Reefat vs Murtas Kazhgaleyev, Asian Championships 2001, Spanish Game: Berlin Defense (C65), 0-1
Joel Lautier vs Murtas Kazhgaleyev, Grand Prix d"Echecs 2004, King"s Indian Defense: Saemisch Variation (E81), 0-1
Teimour Radjabov vs Murtas Kazhgaleyev, FIDE World Cup 2005, Spanish Game: Exchange (C69), 0-1
Murtas Kazhgaleyev vs Pawel Jaracz, Ordix Open 2008, Nimzo-Indian Defense: Classical Variation (E32), 1-0.