Nigeria were leading Group C going to Tuesday's match with 12 points but Cape Verde were also determined to get a spot in the playoffs for Qatar 2022.
Gernot Rohr's men needed a win or a draw to qualify for the playoffs while Cape Verde needed a win to pip the top spot from Nigeria.
Osimhen gave Nigeria the needed edge when he scored in the first minute of the match but Cape Verde replied back with a goal in the 6th minute of the game.
With 2 goals in the first 6 minutes of the game, it was assumed that it was going to be a goal-fest in Teslim Balogun Stadium in Lagos but the match ended with lone goal from both teams.
Osimhen took his tally to 19 caps, 10 goals, 5 assists for Nigeria and Rohr's men looking forward to joining nine other teams in the playoffs next March for a place at Qatar 2022.