Sara Ege, 33, beat Yaseen Ege to death at their home in Pontcanna, Cardiff, in July 2010 and set fire to his body.
She was also found guilty of perverting the course of justice at Cardiff Crown Court. Sentence was adjourned.
The boy's father, Yousuf Ege, 38, was acquitted of causing Yaseen's death by failing to protect him.
It was initially thought Yaseen had died in the blaze at the family home but tests later revealed he had died hours earlier.
His mother had pleaded not guilty to his murder and claimed her husband was responsible for Yaseen's death.
She said she feared her husband would kill her and target her family unless she confessed to the murder.
That confession - made to police days after the death of her son - was captured on video and played to the jury during the five week trial.
During the hour-long harrowing footage, university graduate Ege described how the young boy collapsed after she had beaten him while still murmuring extracts of the Koran.
"He was breathing as if he was asleep when I left him," she said.
"He was still murmuring the same thing over and over again. I thought that he was just tired."
When she returned 10 minutes later she found her son shaking and shivering on the floor. He then died.
Within moments she said she decided to burn his body and ran downstairs to get a lighter and a bottle of barbecue gel.
'He never complained'
In police interviews she also confessed to beating her son for no reason and that her anger often led to her being out of control.
She and her taxi driver husband had enrolled Yaseen in advanced classes at their local mosque as they wanted him to become Hafiz - an Islamic term for someone who memorises the Koran.
The court heard Ege become more and more frustrated with her son's inability to learn the passages he needed to.
She told officers: "I was getting all this bad stuff in my head, like I couldn't concentrate, I was getting angry too much, I would shout at Yaseen all the time.
"I was getting very wild and I hit Yaseen with a stick on his back like a dog."
She later retracted her statement.