A 5-year-old on Staten Island hopped into the driver’s seat of a van with its engine running, somehow threw it into reverse gear and caused it to run over a 2-year-old boy, critically injuring him, law- ­enforcement sources said.

The older child managed to get ­behind the wheel while a woman was strapping another youngster into the back seat of the van, which ­belongs to nearby Busy Kidz Group Family Day Care, according to the sources.

The woman had been transporting children when the 2-year-old was hit, witnesses said.

The boy was rushed to Richmond University Medical Center, where he was listed in critical condition, according to police.