The other opening-round Group A match was equally close with Burkina Faso scoring midway through the second half for a 1-0 victory over Zimbabwe.
Walaa Mohamed levelled for All-Africa Games football debutants Sudan only for Bidimbou to snatch the match-winner three minutes before half-time.
Congo Brazzaville staged and won the first All-Africa Games football tournament 50 years ago, winning the final against Mali 7-1 on corners after a goalless draw.
Sydney Mohamed Sylla was the Burkina Faso match-winner, claiming the only goal after 63 minutes for a nation who upset Ivory Coast to reach Brazzaville.
Football action resumes Wednesday with a Group B fixture between arch-rivals Ghana and Nigeria, who are considered strong contenders for the gold medals.