Ukraine made the trip without coach Oleg Blokhin, who underwent surgery to remove a blood clot from a carotid artery earlier this week, days before he planned to step down anyway in order to return to Dynamo Kiev.
Blokhin's absence dominated the agenda in the build-up to the match and although the players had insisted it would not affect them, they certainly looked far from their best as they fluffed their chances to give Moldova a first point of the campaign.
Not that they did not create plenty of openings in a match that was one-way traffic throughout.
Roman Zozylya wasted some of the best, blazing over from close range midway through the first half and then heading against a post from Ruslan Rotan's 34th-minute free-kick.
Early in the second half, Stanislav Namasco pushed Denys Garmash's header around the post before Taras Mykhalyk wasted another close-range chance.
There was a late chance for Moldova, but Andrei Pyatov parried Alexandru Gatcan's shot away from danger.
Ukraine have two points from as many matches after their opening 1-1 draw with England.