Police were called to the property in Arthur Road in the West Sussex town at 5.30am on Sunday where the victim died, despite efforts of officers and paramedics to save his life.
A Sussex Police spokesman said: “A swift police response led to the arrest of two people in connection with a violent incident in Crawley on Sunday morning.
“Officers responded to a report of a stabbing at a block of flats in Arthur Road around 5.30am.
“Despite the best efforts of police and paramedics, who commenced emergency first aid, a man in his 20s was sadly pronounced deceased.”
“His next of kin have been informed and are being supported by specialist officers at this time.
“Searches including a police drone and the National Police Air Service helicopter were carried out.”
“This resulted in the arrest of a 22-year-old man from London and a 23-year-old man from Crawley on suspicion of murder. They have been transported to custody.”
Detective Superintendent Andy Wolstenholme said: “We are treating this as a targeted attack with no threat to the wider community, and we are not seeking anyone else in connection with it at this time.
“This is a fast-moving investigation and the public can expect to see an increased police presence in the area in the meantime. Please come forward if you have any information that could assist us.”