He was the coach of Mikhail Tal and Garry Kasparov, both of whom are considered to be among the greatest chess players of all time.

[1] He showed chess talent as a youth, and came under the wing of the master and trainer Vladimir Makogonov.

Bagirov qualified for the final for the first time in 1960, and finished in 4th place at the 27th USSR Championship in Leningrad, which was won by Viktor Korchnoi.

Bagirov moved into training work in the 1970s, and for a short time in 1975, as Azerbaijan national coach, was the sole trainer of future world champion Garry Kasparov.

Following a dispute with chess officials, Bagirov moved to Latvia in the late 1970s, and coached former world champion Mikhail Tal, and future grandmasters Alexei Shirov and Alexander Shabalov.