The winger coolly slotted home Youcef Belaili’s cutback to open the scoring in the Group A decider just after the 20-minute mark, claiming an 11th goal in his last 12 international appearances in the process.
But the visitors, who had also remained unbeaten in qualifying before their latest showdown with the Desert Foxes, were level before half-time thanks to Zakaria Sanogo’s first goal for his country.
Djamel Belmadi’s men knew they would reach the next stage of qualifying if they could avoid defeat, and they gave their prospects a major boost with 20 to play when Sofiane Feghouli got their noses back in front.
Nonetheless, Burkina Faso once again responded in Blida, with Issoufou Dayo tucking home from the penalty spot to set up a grandstand finish.
But the visitors couldn't find the all-important winner at the Mustapher Tchaker stadium, meaning Mahrez and co. move into the final stage of African qualification for next winter's tournament in Qatar.
Doyle played the full 90 minutes and grabbed two assists for Lee Carsley’s youngsters but was unable to prevent his side from being edged out 3-2.
The hosts had taken a three-goal lead into the final ten minutes before the Hamburg loanee fed both Stuttgart’s Clinton Mola and Crystal Palace defender Marc Guehi from corners to give England hope of an unlikely comeback.
Harwood-Bellis, under the watchful eye of Vincent Kompany while on loan at Anderlecht, was brought on for the final 20 minutes of the match, replacing Sheffield United’s Rhian Brewster.