Liverpool manager Benitez has also signed forwards Fernando Torres and Andriy Voronin this summer.
But there is little in Mr Voronin's economic programme to suggest that a reunited Moldova would live any better than a disunited one.
Voronin fired just wide from 22 yards and then forced Gordon into a nervous save from a similar distance as Ukraine continued to dominate possession.
BBC: SPORT | Football | Internationals | Scotland 3-1 Ukraine
But calamitous Luton defending on 72 minutes let substitute Andriy Voronin break free and, though his shot was saved by Brill, Crouch fired home the rebound.
Voronin has been on holiday in Miami over the Christmas period, having been frozen out by Benitez since a disappointing appearance in the Champions League draw in Lyon.
Although Moldova has no aspirations to join NATO, it is keen to get into the EU. Its president, Vladimir Voronin, met his Russian counterpart, Dmitry Medvedev, in late August.
Liverpool then attempted to make their most of their numerical advantage, with Riise shooting wildly over when unmarked and then Voronin having a shot blocked by Howard from close range.
Benitez's side started better and should have taken the lead in the fourth minute when Andriy Voronin shot straight at Everton keeper Tim Howard after Hibbert's hesitation let in Yossi Benayoun.
Newspaper reports have linked the Dutch pair with loan moves to Liverpool, while speculation has also focused on the possible departures from Anfield of Andriy Voronin, Andrea Dossena and Philipp Degen.
Ukraine squandered a chance to level when defender Volodymyr Yezersky found himself with only goalkeeper Craig Gordon to beat in front of goal but failed to gather a Voronin up and under.
BBC: SPORT | Football | Internationals | Scotland 3-1 Ukraine
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