Akinbiyi became the Foxes record signing under former manager Peter Taylor when he joined from Wolves for £5million in 2000.
But in 19 months at the club he managed just 13 goals in 67 appearances before he was unloaded to Crystal Palace for £2.2million.
City took to the field with the same eleven which had started in the 2-1 win at Watford. It was the first time this season that Craig Levein had stuck with an unchanged team.
Leicester dominated from the start but failed to make much of an impression on the Burnley goal.
Despite all their possession, City had to wait until the 18th minute for their first worthwhile attempt when Elvis Hammond seized on a misdirected back pass and surged forward before unleashing a 16-yard shot which John McGreal managed to deflect for a corner.
Hammond then dropped a shoulder and jigged inside a defender before testing the keeper from just inside the box.
It was all Leicester midway through the half Mark De Vries screwed a 12-yard effort wide as his side increased the pressure on Burnley's overworked rearguard.
Before the break the visitors only outlet were hopeful punts towards Akinbiyi who was subjected to a chorus of boos each time he touched the ball.
Burnley had not managed to produce a single effort on goal during the first half, but within seconds of the restart James O'Connor had powered in a 22-yard shot straight at Rab Douglas.
The second half was a much more even affair with Burnley prepared to push forward in greater numbers.
On 55 minutes James O'Connor again tried his luck from a distance this time his shot flew narrowly wide.
Burnley continued to threaten and only a late block by Dion Dublin denied Garreth O'Connor from sixyards out.
But there was no denying Burnley on 64 minutes with Akinbiyi registering his eighth goal of the season.
James O'Connor's shot skidded across the face of the goal with Akinbiyi ghosting in at the far post to steer the ball home.
Substitute Iain Hume sent a header wide and De Vries failed to find the target from 12 yards as City fought desperately to get back on level terms.
They virtually laid siege to the visitors' goal in the closing stages but failed to muster a sniff of a breakthrough until the 86th minute, when Patrick McCarthy's header from Momo Sylla's corner looked a goal all the way until Brian Jensen twisted in midair to claw the ball from under the bar.