They were tracked down with the help of police dog Ellis in the early hours of Wednesday morning.
Police were called to Compton Road, in Cradley Heath, in the early hours to reports of a burglary in progress.
Police said as officers arrived a red Skoda was leaving the scene. Following a pursuit, the car was abandoned on Stretton Place, in Netherton, Dudley, and a group of men were seen running from the car.
A 23-year-old was quickly detained and arrested, said West Midlands Police.
The car, which was believed to be on false plates, was searched and a large Rambo knife was found nearby, said a force spokesman.
Police dog Ellis was set to track the other occupants of the car and after venturing deep into Netherton Park, the pup found a 21-year-old hiding in dense undergrowth.
He was arrested on suspicion of possession of an offensive weapon and vehicle theft.
While a third man was arrested in Handsworth after a suspected stolen Ford Fiesta failed to stop of officers and was found abandoned in Crick Lane.
Police dog Arnhem tracked down the 20-year-old who was hiding on the top of a first floor roof, covering in branches.
He was arrested on suspicion of vehicle theft.
All three remained in police custody on Wednesday.