Piotr Skut left the toddler badly injured while he was supposedly caring for her at his home in Glasgow's Townhead last April.
The child later required extensive surgery - but Skut denied having hurt her, claiming he had found her bleeding.
Skut, 29, claimed the youngster could have fallen against a stool. But the Pole was snared after his DNA was found on the girl's body.
Skut attacked the girl just weeks after a video clip showing similar abuse was downloaded onto his computer.
A jury yesterday unanimously found Skut guilty of indecently assaulting the child to her severe injury.
Judge Lady Dorrian remanded him in custody following the trial at the High Court in Glasgow.
Skut's wife wept and blew him a kiss as he was led, handcuffed, down to the cells.
He faces a lengthy jail term when he returns to the dock next month.