But Osako produced a smart turn and finish inside the box to equalise for Japan 10 minutes into the second half following sustained pressure from the four-time Asian champions.
The Japanese are seeking to make up for their Asian Cup flop four years ago when they lost on penalties to United Arab Emirates in the quarter-finals.
But with a little luck Turkmenistan could easily have inflicted a major shock.
The Emeralds should arguably have been three up by halftime after Mekan Saparov headed over from point-blank range and an Atayev rocket forced Japan goalkeeper Shuichi Gonda into a brilliant reflex save.
"We lost our way a bit in the second half, but we're not out of it yet. We'll give everything in the next two games."
Japan, only kept out of the World Cup quarter-finals by a stunning Belgium comeback from two goals down, have now lost just one of their last 29 games at the Asian Cup, excluding penalty shootouts.
But they will need to improve if they are to threaten favourites Iran -- 5-0 winners over Yemen earlier this week -- and a South Korea side soon to be boosted by the arrival of Tottenham forward Son Heung-min.
"The first match is always a bit special and we expected a battle," said Moriyasu.
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