The white Hyundai was stolen on Hume Street on Sunday.
Police spotted the vehicle joining the A38 towards Birmingham just before 9.15pm yesterday.
It fled from officers, who chased the car towards Aston Lane in Perry Barr.
The car then crashed into a parked car on that street, causing minor injuries to the people inside.
Armed officers then arrested a 40-year-old man on suspicion of robbery and a 38-year-old woman on suspicion of taking a vehicle without consent.
West Midlands Police confirmed that they are both currently in custody.