Platonov first made a significant mark in competitive chess in 1958, when at age 24 he posted an even score of 6.5/13 in the Kiev Championship to tie 8th-9th places; the winner was Yuri Nikolaevsky.
In the Spartak Club Championship, Minsk 1962, Platonov scored 8/17 for a tied 11th-13th place; the winner was Anatoly Bannik.