Police said the Toyota had failed to stop for officers on the M621 as it travelled towards the M62 at Birstall at about 14:55.
A pursuit was authorised and the car drove at speed on to the M62 heading towards Manchester.
Police said the Peugeot driver had suffered serious injuries in the crash and his condition in hospital was critical but stable.
The eastbound carriageway of the motorway was reopened at about 20:20, but police said the westbound carriageway would remain closed until the early hours of Sunday as an investigation continued.
The force added the Independent Office for Police Conduct had been notified as was standard procedure for an incident of this nature.
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