Officers say they originally attempted to stop the car following an "altercation" on the Promenade in Blackpool at around 9.55pm.
The car containing two men then made off at speed.
Police later sighted the car in the Wesham area where it was brought to a stop using preemptive tactics.
A spokesman for Lancashire Police said: "We tried to stop the car in Blackpool but it made off at speed.
"The car was spotted later on Fleetwood Road. We used a stinger to bring it to a stop at around 11.30pm.
"The driver was arrested but the passenger made off - he was arrested a short time later."
Both men remain in custody this morning.