Following their 1-1 draw with Congo in the tournament opener, Esteban Becker's men were subject to sustained pressure during the opening half as Burkina - finalists two years ago - sought to bounce back from their opening loss to Gabon.
But, as on that occasion, wasteful finishing undermined their efforts after Alain Traore twice struck the post before half-time.
Guinea attackers Emilio Nsue and Iban Edu schemed inventively throughout and impressed during a more even second period.
Kike and Viera Ellong came closest to securing a famous victory before Alain Traore fluffed his lines once more to leave Burkinabe sweating on the clash between their other group rivals later on Tuesday.
Bakary Kone required a perfectly timed challenge to deny Nsue in the fourth minute before Burkina Faso proceeded to control the opening exchanges.
They almost edged ahead in the 18th minute as Alain Traore clipped a 25-yard free-kick against the post when Equatorial Guinea goalkeeper Felipe Ovono scrambled behind an over-manned wall.
Diosdado Mbele was a touch fortune to escape with only a yellow card - one that will rule him out of the host's final home game - when he cynically ended Jonathan Pitroipa's darting break towards goal.
With half an hour played, Aristide Bance crashed another free-kick goalwards, with Ovono pushing clear before his opposite number Germain Sanou was forced to divert an angled shot from Guinea full-back Sipo behind.
As half-time closed in, Burkina ramped up the pressure - the post denying Alain Traore again as his controlled volley struck Ovono's leg and the inside of the upright before ricocheting clear.
Ovono thwarted Bertrand Traore as he charged towards goal in the 40th minute, with the same player having a close-range shot blocked before Nsue forced Burkina defender Steeve Yago into similarly evasive action at the other end.
There were chances at either end in a fast-flowing opening to the second half - Kike smashing a volley over at the back post for the hosts after Nsue and Iban Edu combined to unlock the Burkina defence.
In the 51st minute, Pitroipa somehow failed to convert Bance's lofted cross with the goal seemingly at his mercy and Alain Traore was soon off-target on the volley.
Equatorial Guinea responded by crafting their clearest chance of the contest.
Javier Balboa capitalised on sloppy play from Djakaridja Kone to set up Ellong, who blazed over from 16 yards.
The host had visibly grown in confidence - Nsue unable to turn home a poorly defended corner and Kike seeing Sanou turn away a drive that bounced awkwardly.
Burkina looked to launch a final sustained assault but found themselves vulnerable on the break, with Kike spurning a good chance as Balboa picked a fine 73rd-minute pass.
Pitroipa, the reigning player of the tournament, had a chance for glory when he cut inside to drive over from inside the box with 14 minutes remaining before Alain Traore side-footed wide under pressure - once again displaying the profligacy that seems set to define Burkina Faso's campaign.
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