The crash occurred around 10:30 p.m. Friday at 17th and Diamond streets in North Philadelphia.
Police said a man carjacked someone earlier and took off with the SUV.
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A nearby pizza shop's surveillance camera captured the stolen SUV slamming into another vehicle.
The impact sent one of the vehicles careening into a 21-year-old woman as she was crossing the intersection.
Police said the stolen SUV driver then got out and fled the scene leaving the woman critically injured.
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She was taken by emergency officials to Temple University Hospital.
Investigators are working to get a description of the suspect.