Moses fell after the merest of touches before calmly stroking the ball into the corner of the net as Polish goalkeeper Bartosz Bialkowski barely moved in Wroclaw.
While friendly results are often misleading, Nigerian confidence will be boosted by defeating a team ranked sixth in the world, 46 places above the west Africans.
It was the second notable friendly scalp for the 'Super Eagles' after a 4-2 triumph over 2014 World Cup runners-up Argentina last year.
Nigeria face the South Americans again during in the group stage in Russia, along with Croatia and Iceland.
Polish star Robert Lewandowski was foiled by the woodwork after eight minutes and had a close-range shot blocked by young goalkeeper Francis Uzoho in the second half.
Morocco were another World Cup qualifier to win in Europe with Khalid Boutaib netting the decisive goal on 40 minutes in a 2-1 win over Serbia in Italian city Turin.
A Hakim Ziyech penalty put the 'Atlas Lions' ahead but Dusan Tadic equalised for Serbia, who haven't qualified for Russia.
Tunisia gave first caps to three France-born players -- defenders Ellyes Skhiri and Yohan Benalouane, and midfielder Seif-Eddine Khaoui -- as they beat Iran 1-0 in Rades.
The trio were eligible because their parents are Tunisian and officials reacted to criticism by saying "they were casting their net wide to ensure all the conditions for (World Cup) success".
The clash of two Russia-bound teams was decided by a Milad Mohammadi own-goal after 71 minutes.
Senegal started with an experimental team that lacked star attacker Sadio Mane and had to come from behind to draw 1-1 with Uzbekistan in Moroccan city Casablanca.
Otabek Shukurov converted a first half penalty and Moussa Konate equalised midway through the second half after slick passing gave him a close-range opportunity.
In friendlies not involving African qualifiers for the World Cup, Mali drew 1-1 with Japan in Belgian city Liege and Gambia were held 1-1 at home by the Central African Republic.
Abdoulaye Diaby scored off a late first half penalty for the Malians, who were deprived of victory by a Shoya Nakajima goal five minutes into stoppage time.
Gambia protested in vain that the Central African Republic leveller by Foxi Kethevoama 15 minutes from time entered the net via the side netting.
Assan Ceesay put the Gambians ahead just before the hour in Bakau, firing a rebound into the net after a penalty had been parried.
A further eight friendlies involving African teams are scheduled for Saturday, including the Ivory Coast against Togo in France and Zambia at home to South Africa.