The Chinese-based pair of Odion Ighalo and John Obi Mikel handed Nigeria a 2-0 half-time lead, before Moses scored in the second half and then set up Kelechi Iheanacho for the fourth goal as Nigeria kept up their 100 percent record in Group B.
Nigeria, who reached the round of 16 at the last World Cup in Brazil, advanced to nine points as they left Cameroon floundering on just two points from three matches at the halfway stage of the group qualifiers.
Cameroon, who have made an African record seven previous World Cup finals appearances and won the African Nations Cup in February, host Nigeria in a return qualifier in Yaounde on Monday.
Obi Mikel's clever punt from midfield set Ighalo away for the first goal in the 29th minute.
The former Chelsea midfielder, captaining Nigeria, scored the second three minutes before half-time with a tap-in from a corner taken by Moses that was allowed to run through by Ighalo's dummy.
Moses, who set the tempo of the home team's attacks, burst from inside his own half to score the third goal after the break and a similar run started the move that allowed substitute Iheanacho to head home in the 76th minute.
The Chelsea winger's absence from Nigeria's last competitive international, a 2-0 home defeat to South Africa at the start of the 2019 Nations Cup qualifiers in June, was all too evident.
Nigeria are now one step closer to reaching the finals, with only the winning teams in the five qualifying groups going to Russia next year.
Algeria and Zambia are the other countries in the group and play in Lusaka on Saturday, where both seek a first victory of the campaign.
(Reporting by Mark Gleeson in Cape Town; Editing by Christian Radnedge)
