Born in St. Petersburg, Ragozin's chess career first came to the fore with a series of excellent results in the 1930s. In the earliest of these, he defeated the respected master Alexander Ilyin-Zhenevsky in a 1930 match and was himself awarded the title of Soviet master. At Moscow 1935, he won the best game prize for his victory against Andor Lilienthal. At the very strong Moscow tournament of 1936, he beat Salo Flohr and Emanuel Lasker and came very close to defeating José Raúl Capablanca, the ever-resourceful ex-world champion scrambling to find a draw by perpetual check at the game's frantic conclusion. There followed a victory at the Leningrad championship of 1936 and second place shared with Alexander Konstantinopolsky (behind Grigory Levenfish) at the Soviet Championship of 1937. At the 1939 Leningrad-Moscow tournament, he finished third equal, behind Flohr and Samuel Reshevsky, but ahead of Paul Keres.