Striker Manucho had twice given Angola the lead, the second from a penalty, in a pulsating game played in front of a disappointingly small crowd at the picturesque Malabo stadium.
Angola have four points from two games in Group B while Sudan have one.
Sudan, champions in 1970, scored their last goal at the tournament against Zaire in 1976.
Since then, they have only qualified once, in 2008, when they lost all three games by a 3-0 scoreline.
Uniquely among the 16 finalists, all 23 of their players are from home based clubs and their starting line-up included seven from last season's African Champions League semi-finalists Al Hilal.
Angola were quick off the mark when Real Valladolid forward Manucho won the ball off Nagmaldien Abdullah, burst forward down the right and scored with a low shot into the far corner in the fifth minute.
Refusing to be overawed, Sudan levelled just after the half-hour when Bashir outjumped two defenders to head in following a cross from the right.
Former Manchester United, Hull City and Panathinaikos forward Manucho put Angola back in front from a penalty shortly after the restart, awarded after Mateus was tripped amid angry Sudanese protests.
Angola then showed their petulant side as two players were booked for time-wasting and paid the price when Bashir took advantage of sloppy defending to hook in the equaliser in the 73rd minute.
