Summer Peace suffered the injuries after being "intentionally shaken" by her father Philip Peace on September 8, 2017 – and died the following day.
Peace, of Himley Road, had denied shaking his daughter, who had become restless, and said he "wouldn't do anything" to hurt her.
Jurors at Birmingham Crown Court unanimously found the 43-year-old guilty of murder and not guilty of the alternative charge of manslaughter after 13 hours and 39 minutes deliberating.
Prosecutors said the father had shaken his daughter in a "whiplash-style motion" which was intentional and caused her the fatal injuries.
Coverage of the case:
Summer, who had breathing difficulties, was rushed to Russells Hall Hospital by paramedics after her collapse at around 4pm and her body starting to become blue – evidence of cyanosis.
She received emergency treatment and was later transferred to Birmingham Children's Hospital at 10.30pm.
Doctors later established the brain injuries “were ones she could not recover from” and it was agreed with her parents that life support would be withdrawn. She died at 5.44pm on September 9, around 25 hours after her initial collapse.
Experts for the prosecution said the reason for Summer's collapse was a result of "head trauma" and not down to acute pneumonia as had been claimed by the defence counsel.
Defence barristers had claimed Peace could have "accidentally" cause his daughter the brain injuries following her collapse, in which he may have picked her up abruptly – and that the movement was without malice as had been claimed by the prosecution.
Before releasing the jury the Honourable Mr Justice Linden, thanked them very much for the diligence they had shown when considering the case.
Peace will be sentenced tomorrow at 10am.