Mohamed Yattara's first-half opener in an entertaining match had threatened a shock until Doumbia's 73rd minute leveller.
The Guineans might rue a missed chance to stun their more heralded rivals, but the result will have further boosted their confidence after they defied the odds to qualify for tournament.
Having overcome the ravages of the Ebola virus in their country which forced them to play all their home qualifiers at a neutral venue, Guinea stunned the Ivorians when Yattara fired them ahead with a superb strike.
Ivory Coast had forward Gervinho sent off for striking an opponent shortly before the hour mark.
Mali and Cameroon, the other two teams in the group, play later on Tuesday.
Ivory Coast's three-pronged attack featuring Gervinho, Salomon Kalou and Wilfried Bony struggled in the first half against a well-organised Guniea defence marshalled by centre back Florentin Pogba, brother of France midfielder Paul.
The tireless Gervinho nearly opened the scoring after one raid in the 17th minute but Guinea keeper Naby Yattara tipped his close-range effort against the crossbar.
Taking every opportunity to break forward, the Guineans delighted their fans in the Estadio de Malabo when Mohamed Yattara blasted an unstoppable shot on the turn into the roof of the net after an Ivorian defender miscued a deep cross from the right into his stride.
Bony, who signed for English champions Manchester City earlier this month, came close with a rasping half-volley from 20 metres shortly after the break.
When Gervinho was shown a red card for an off-the-ball incident it fired up the Guinea side and they almost doubled their lead when Ibrahima Traore weaved his way past three markers and hit the crossbar with a delightful curling shot.
They paid a heavy price for that ill fortune when midfield powerhouse Yaya Toure found his soon-to-be team mate Bony with a defence-splitting pass and the burly striker laid it on perfectly for Doumbia to sidefoot home the equaliser.
Both sides threw men forward in search of a winner with Ivory Coast looking the more likely team to score but Guinea, clearly running out of steam, held on.
(Writing by Zoran Milosavljevic; Editing by Martyn Herman)
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