Two men were found in the street and another in a back garden on Goldthorn Hill in Goldthorn Park at about midnight.
A member of the public flagged down a police car and the men, aged 27,31 and 36, were taken to hospital with serious injuries.
The road has been cordoned off while police investigate.
Sgt Carl Russell said: "Several people have told us that a car was seen to speed away from the scene shortly after the attack.
"We are appealing to anyone who may have seen this car to come forward with information.
"The injured men are in a serious condition and continue to be treated in hospital."
Three men have been stabbed in an attack at a house in Wolverhampton.