Turov participated in the 1st Children's Chess Olympiad, held in Linares in 1993, as part of Russia "A" team, which won the gold medal.

[7] In 2010, he won the Chennai Open,[8] tied for 1st–4th with Sergei Zhigalko, Rinat Jumabayev and Vitali Golod in the 4th Georgy Agzamov Memorial in Tashkent, winning the tournament on tiebreak,[9] tied for 1st–6th with Dmitry Kokarev, Alexey Dreev, Martyn Kravtsiv, Baskaran Adhiban and Aleksej Aleksandrov in the 2nd Orissa Open tournament in Bhubaneshwar.

[10] In 2011 he tied for 2nd–6th with Konstantine Shanava, Mikhail Ulibin, Robert Hovhannisyan and Levon Babujian in the 4th Karen Asrian Memorial in Jermuk,[11] tied for 2nd–7th with Julio Granda, Aleksander Delchev, Ivan Šarić, Pablo Almagro Llamas and Mihail Marin the 31st Villa de Benasque Open[12] and tied for 2nd–7th with Deep Sengupta, Viacheslav Zakhartsov, Krisztian Szabo, Lev Gutman, Dávid Bérczes and Samuel Shankland in the ZMDI Schachfestival in Dresden.

[13] In January 2012 Turov won the Group C of the Tata Steel Chess Tournament in Wijk aan Zee.

[15] In 2014, he tied for 1st–3rd with Jan Werle and Yuri Solodovnichenko in the Oslo Chess International GM Tournament.