He was awarded the International Grandmaster title in 1952 and played in the Candidates Tournament in Zurich in 1953, where he tied for eighth place. From 1946 to 1956, he was among the world's top ten players. He played in 23 USSR Chess Championships (a record equalled by Efim Geller), tying for first place twice. In 1952 he lost the playoff match to Mikhail Botvinnik, while in 1956, he beat Yuri Averbakh and Boris Spassky for the title. He is probably best known for his 6-0 loss to Bobby Fischer in the 1971 World Championship Candidates match. However, few players have beaten six world champions (Botvinnik, Vasily Smyslov, Mikhail Tal, Tigran Petrosian, Spassky, and Anatoly Karpov) as Taimanov has.
After his loss to Fischer, the Soviet government was embarrassed, and, as Taimanov later put it in a 2002 interview, found it "unthinkable" that he could have lost the match so badly to an American without a "political explanation". Soviet officials took away Taimanov's salary and no longer allowed him to travel overseas. The official reason given for punishing Taimanov was that he had brought a book by Aleksandr Solzhenitsyn into the country, but that explanation was secondary in nature. The officials later "forgave" Taimanov, and lifted the sanctions against him. Fischer's 6-0 win against Bent Larsen later in 1971 may have helped change their minds.
He has opening variations named after him in the Sicilian Defence, Benoni Defence and Nimzo-Indian Defence. He has written books on both of his named variations, as well as an autobiographical best games collection.
With his wife, Lyubov Bruk, he formed a piano duo, some of whose recordings were included in the Philips and Steinway series Great Pianists of the 20th Century.