The victims, aged 26, 37 and 39, were set upon by two men armed with knives in Southall Road in Ashmore Park, Wednesfield, after leaving a pub.
Armed offices rushed to the scene at around 10.55pm after receiving numerous 999 calls to report a fight between a group of people armed with weapons.
The hunt for the culprits continue while the three victims, who are all from Wolverhampton, remain in hospital and undergo treatment for their injuries.
Residents nearby said the incident just seemed to "escalate out of hand and they were waving weapons around" and described it as a "scary experience".
The force said officers believed all of the men were known to each other.
Cordons were set up at the Southall Road junctions with Ecclestone Road and Griffiths Drive afterwards.
Detectives are actively searching for two suspects, who were described as wearing black clothes, and searches have been carried out at multiple addresses in the city.
Anyone with information is urged to contact the officers via the force's Live Chat quoting reference number 4513-240622.
Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org