The Russian-based forward struck either side of halftime as the Super Eagles, who began the tournament with a 3-1 defeat against Egypt, made sure of a top-two finish in Group C.
Obafemi Martins completed the scoring just before the end for the World Cup qualifiers who had needed only a draw to go through.
Mozambique, who have taken part in the tournament five times without mustering a win, finished with a single point from their opening draw with Benin.
"This victory will bring back the needed confidence in the team as we await our quarter-final opponents," Nigeria coach Shaibu Amodu told a news conference.
"Let me say that for now I do not want to jump the gun. Let me savour this victory first, when we get to that bridge of who to face, we will cross it."
BEST CHANCE
The match got off to a lethargic start while the out-of-tune trumpets of the usually irrepressible Nigerian supporters' band were drowned out by the monotonous drone of plastic horns.
Chinedu Obasi should have given Nigeria the lead but headed weakly into the arms of Mozambique goalkeeper Kampango from point-blank range.
Odemwingie sounded his first warning when he turned his marker and rifled in a low shot which Kampango did well to turn around the post before Obasi fired a volley just wide.
In between, Paito had Mozambique's best chance, a 30-metre effort which was parried by Vincent Enyeama.
Nigeria went ahead just before halftime when Odemwingie collected the ball outside the area and scored with a left-foot shot which found its way between Kampango and his near post.
Two minutes after the restart, Odemwingie struck again, turning in an easy chance after Yakubu Aiyegbeni broke down the left.
That ended the game as a contest and Martins completed the scoring when he hammered home a rebound after John Obi Mikel had dispossessed a defender and seen his shot saved by Kampango.
