West Yorkshire Police said it happened at 00.44 GMT, when a blue BMW 123D failed to stop for police in Gelderd Road. It then crashed into a white Volkswagen Scirocco.
The driver and passenger travelling in the Volkswagen, a 22-year-old man and 23-year-old woman, both from York, died at the scene.
The occupants of the BMW, a 39-year-old man from Harrogate, two boys aged 16 and 17 and a 16-year-old girl, have been arrested on suspicion of causing death by dangerous driving.
The 39-year-old is also being held on suspicion of driving while over the prescribed limit for cannabis, the force confirmed.
A scene and road closure remain in place in Gelderd Road, and drivers are advised to avoid the area and seek alternative routes.
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