The car was kept in sight as the driver turned off on to SH2 at Bay View and headed for the city.
Traffic was not heavy at the time.
"The left front tyre had come completely off and he was driving on the rim," Napier Police Inspector Kevin Kalff said.
The man gave up the chase near the intersection of Douglas McLean Ave and Latham St.
"He ran off and made his way through several properties," Mr Kalff said.
Police cordoned the area and a dog team was called in.
The 21-year-old man was found and arrested a short time later and was scheduled to appear in the Napier District Court today.
He was charged with unlawfully taking a motor vehicle, dangerous driving and failing to stop.