The 21-year-old's bid to escape in his grey Vauxhall Vectra failed when it careered on to the pavement and became jammed between a wall and a tree.
He tried to make a run for it but pursuing police managed to catch and arrest him in Emscote Street South, Bell Hall, Halifax, at 4.15pm on Thursday.
Earlier, police had been following the car when it suddenly sped off.
Residents spoke of their shock.
Tracy Mallinson, 44, of Emscote Street South, said: "I was dozing on the couch when I heard a big bang. It shook the house. The dog jumped a mile off the sofa and I shot to the window to see the car there.
"They drove the car up the path and just missed another vehicle with children inside.
"Police came from both sides and chased two men who had scarpered. Everything happened so quickly. But it could have been worse as my son lives in the basement."
John Shoesmith, 52, of Pellon Lane, was getting a haircut on Emscote Street South when he saw the crash.
He said: "Police arrested one person and another ran away.
"The car was wedged in between a garden wall and a tree. It looks like it was being driven down the pavement.
"The front of the car was crumpled in.
"It is quite a quiet area here and you don't expect to see something like this here."
Tom Stanley, 17, of Emscote Grove, said: "It was a bit shocking."
A police spokeswoman confirmed a 21-year-old man had been arrested on suspicion of possessing an offensive weapon and suspected cannabis, dangerous driving, driving while disqualified and without insurance.
He has been released on police bail pending further inquiries.