In 1938, at nineteen, he won the Ukrainian Championship; the following year he won the Ukraine SSR championship, qualified to play in the USSR Chess Championship at the age of 20, and gained his national chess master title. He earned a degree in philology at Sverdlovsk University.
In 1940, Boleslavsky played in the 12th USSR championship final in Moscow. He won eight of his last ten games and tied for fifth/sixth place. At the end of 1940 he won the Ukrainian Championship for the third consecutive year. In March 1941, he took part in the match-tournament for the title of Absolute Champion of the USSR, finishing fourth of six participants. On the eve of the match-tournament, he had to pass an examination at the University, and his preparation for the chess event proved to be inadequate.
In 1945 he took second place in the 14th USSR championship, behind Mikhail Botvinnik and was awarded the Grandmaster title in the USSR. He made his international debut on third board of the USSR–USA radio match. He drew his first game with Reuben Fine and defeated him in the second game, winning a prize for the best game of the match. Boleslavsky secured a clear advantage in the opening thanks to his superior pawn structure and won without allowing Fine much counterplay. The Soviets regarded Fine as possibly the strongest American player based on his international results in the pre-World War II era.
In 1946, his daughter Tatiana was born; she later married David Bronstein. Boleslavsky and Bronstein had become friends in the late 1930s, and remained so throughout their lives. In 1946, Boleslavsky played abroad in an international tournament for the first time in Groningen and tied for sixth/seventh place. In 1950 Boleslavsky was awarded the title of International Grandmaster title from FIDE.
Boleslavsky qualified from the first-ever Interzonal at Saltsjöbaden 1948 into the Candidates Tournament two years later in Budapest. In the Candidates tournament—the winner of which would play a Championship match against Botvinnik—Boleslavsky was the only undefeated player, and led for most of the tournament, but in the last round he was caught by Bronstein.
From the start of the tournament Boleslavsky forged into the lead and by the end he was half point ahead of his closest rival, Bronstein. In the final round he played Gideon Stahlberg of Sweden who was having a poor tournament and so thought he could count on victory and a match with Botvinnik. Thinking Bronstein would be unable to win his last round game against Paul Keres, Boleslavsky made a quick draw with Stahlberg while Bronstein sacrificed a Pawn, developed a formidable attack and won. The result was a tie for first between Boleslavksy and Bronstein. Bronstein won a playoff in Moscow (+3 −2 =9).
This turned out to be Boleslavsky's last chance as a serious contender for the world championship. In 1953, he participated in the Candidates' tournament in Zürich, but finished in 10th–11th places, and never qualified for subsequent world championship cycles.
In 1951, Boleslavsky was Bronstein's second during his match with Botvinnik for the world championship, which wound up drawn after 24 games. In 1952, he scored 7 out of 8 at the Helsinki Olympiad. This was the only Olympiad he would play in his career, but he attended several others to provide support for the Soviet team. He won the Belarusian Championship in 1952 (joint) and 1964.
In 1961, he played in his last USSR Championship final. He took first place at an international tournament in Debrecen. He was world champion Petrosian's assistant from 1963 to 1969.
In 1968 he captained the USSR students' team, which won the World Championship at Ybbs. His last tournament appearance was in Minsk in 1971, at age 52. Boleslavsky was the chief trainer of the Soviet Chess Federation in the 1960s, and he remained until his death a very well respected analyst and chess writer, particularly in opening theory.
He died in Minsk on February 15, 1977, at the age of 57, after falling on an icy sidewalk, fracturing his hip and contracting a fatal infection while in hospital.
One of Boleslavsky's main contributions to opening theory is the Boleslavsky Variation in the Sicilian Defence (1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 Nc6 6.Be2 e5). Boleslavsky, together with fellow Ukrainians Bronstein, Efim Geller, and Alexander Konstantinopolsky, beginning in the late 1930s, turned the King's Indian Defence from a suspect variation into one of the most popular defences today. Hans Kmoch in his book Pawn Power in Chess calls the King's Indian configuration of black pawns on c6 and d6 (especially if the d-pawn is on a semi-open file) "the Boleslavsky Wall".
Boleslavsky’s play was distinguished by his extraordinary speed of play, often using less than an hour. His outstanding natural talent allowed him to retain in memory a very large number of games. A taciturn player, he was always a very dangerous opponent with first class opening preparation. He was admired for the depth of his strategic plans and the beauty of his sudden tactical attacking moves.
Lev Polugaevsky said of him, "I am convinced that any player, even the very strongest, can and should learn from his games (especially the Sicilians!). As regards his depth of penetration into the mysteries of the Sicilian Defense, for both sides moreover, it is doubtful if anyone could compare with Boleslavsky. He had a virtuoso feeling for the dynamics of the opening, and always aimed for a complicated and double-edged struggle, although by nature he was one of the most modest grandmasters with whom I have had the pleasure of rubbing shoulders." A book of his best games, published in 1990, won the prize as the best chess book published in Great Britain that year.