Pirog improved his perfect record to 20 wins but he could not add a 16th knockout to his impressive tally as the bell came too early in the Russian capital.
Pirog had gradually softened up his opponent over the course of 12 rounds, but a telling blow did not materialise, leaving the judges to score the fight 120-108, 119-109, and 118-111.
"Everything we planned with the team - huge thanks to them - we pulled off with top marks," Pirog said.
"I've said time and again that this is a really tricky opponent, and that the number one goal wasn't just to have an exciting match, but to win, and we did that."
Pirog said a unification fight with Australia’s IBF champion Daniel Geale was now "90 per cent certain" to take place in the United States in late August.
Defeat for Ishida left him with a record of 24 wins from 34 fights.