The Chelsea midfielder earned and scored both spot kicks as the Super Eagles safely qualified from Group C and sent the Walya Antelopes out of the tournament.
Celtic’s Efe Ambrose had a golden opportunity on two minutes, but he flashed a free header just over Sisay Bancha’s bar.
Nigeria controlled much of the early exchanges and restricted Ethiopia to only a few chances, with Saladin Said’s 15th minute header the best of their opportunities.
But Ethiopia nearly took an unlikely lead on the half hour, however Getaneh Kebede failed to connect with Yussuf Saleh’s dangerous free kick.
Ethiopia’s near-miss seemed to spur on the Super Eagles and only the safe hands of 23-year-old Bancha denied both Echiejile and Moses.
On 40 minutes, the Walya Antelopes had another clear chance as Saladin drifted into Nigeria’s box only to see his shot blocked by Kenneth Omeruo.
Both sides enjoyed early chances at the start of the second half, Omeruo’s fantastic block denied Saladin a diving header before the Nigerian defender nodded just over from Moses’ corner.
Nigeria came close on 65 minutes as Godfrey Oboabona saw his attempt cleared off the line before Sunday Mba’s long-range effort stung Bancha’s fingers.
But the Super Eagles pressure paid dividend on 79 minutes as 22-year-old Moses calmly slotted home from the spot after he was brought down by Alula Girma.
Within a minute of the Chelsea man’s goal, the Ethiopians were nearly level though, only the athleticism of Vincent Enyeama denied Saladin from point blank range.
However with five minutes left, Nigeria sealed the victory as Bancha’s reckless challenge on Moses warranted both a second yellow and a penalty.
And Nigeria’s number 11 stepped up once again and dispatched the ball low past stand-in keeper Addis Hintsa to secure all three points.
A goalless draw between Burkina Faso and Zambia means the Super Eagles qualify second in Group C and will now face a tough quarter-final test against Ivory Coast.