The centre-back headed in 15 minutes from time to cancel out a fine free-kick from Benjamin Moukandjo as both sides shared a point in their tournament opener at Stade d'Angondje.
These two finished top of their respective qualifying groups and it was a suitably even contest in Libreville, with both goalkeepers kept busy behind some less-then-convincing defences.
Alain Traore went close to an opener for Burkina Faso before Moukandjo's superb strike put Cameroon in the ascendancy, and only two excellent saves from Kouakou Herve Koffi and a glaring miss from Clinton N'Jie kept Paulo Duarte's side in the contest heading into the last half-hour.
Cameroon - who have now only won one of their last nine matches at AFCON finals - were made to pay for those missed opportunities when Dayo steered home from close range.
The result puts Burkina Faso, Cameroon, host nation Gabon and Guinea-Bissau all level on points and goal difference, after the earlier match had also finished 1-1.
Jonathan Pitroipa volleyed in from an offside position after six minutes to show a glimpse of Burkina Faso's threat on the break, and Fabrice Ondoa was forced into a brilliant reaction save to keep out Traore's free-kick soon afterwards.
Cameroon's first opportunity came through Christian Bassogog, who cut in from the right wing and rippled the side-netting after a fine throughball from N'Jie.
Bassogog was proving a handful, and another clever run and cross forced Koffi into a smart stop, but the goalkeeper could do nothing to deny Cameroon an opener after 35 minutes.
Jacques Zoua won a free-kick 20 yards from goal, and Moukandjo whipped a superb strike into the left-hand corner.
A smart stop at the near post from Koffi prevented N'Jie from doubling the lead and the goalkeeper raced off his line to make a crucial challenge on Bassogog a few seconds before the break, with the Cameroon winger taken off on a stretcher soon afterwards.
Bertrand Traore had Ondoa at full stretch after the restart but Moukandjo - back on and seemingly fully fit - continued to trouble the Burkina Faso defence with his runs through the middle.
It was N'Jie who wasted the next clear chance to double the lead, however. Zoua's thunderbolt from 25 yards was only parried by Koffi and the man on loan at Marseille from Tottenham scuffed the rebound wide of the far post with the goal gaping.
That miss proved costly for Cameroon as Burkina Faso snatched an equaliser with 15 minutes to play. Substitute Banou Diawara's free-kick was beaten out by Ondoa, and as Bakary Kone nodded the rebound back towards goal, Dayo met the ball first and headed it into the top corner.
Bassogog shot wide from distance as both Cameroon boss Hugo Broos and Duarte made attacking changes late on, but a decisive third goal proved elusive.