A first-half brace from Rangers striker Alhaji Gero put the Nigerian youngsters in the driving seat, and they held on for the win despite Alhaji Said's pull back in the second half.
"It was a good game but the home team came out the stronger in the second half. They had the advantage of having already started the qualifiers before us and also they were playing at home," Obuh said.
"But we knew we had to win this match even against a very smart Tanzanian team, who at a time almost got my team to play their long ball tactics.
"All the same, we still have a second leg to play, but we expect to reach the next round of the competition."
The second leg will be played at the Ilorin Stadium on August 11.
The winners of the tie will face the winners of another second round match between South Africa and Congo.
Congo won the first game at home 2-1.