An Chicago police officer was wounded in that exchange and one of the suspects was killed.
It started with the stabbings in the 5800-block of North Winthrop -- two people were killed and one was critically injured.
After the suspects fled, the officer was shot near Broadway and Thorndale.
The suspects were eventually stopped at Devon and Greenview. One was shot and killed.
On Sunday afternoon, investigators say the attacks may be tied to a series of other drug-related slayings.
A shaken Mohaed Yusuf talked about the gruesome discovery he and his neighbor made at the North Side apartment building they call home.
"My friend, he checked the person. He saw the man cut, his throat just cut," Yusuf said.
On Saturday afternoon, Yusuf says he heard a "strange" bumping noise against the wall, then opened the front door to find a severely injured man.
"Still alive and walking, but handcuffed by duct tape, you know," Yusuf said.
Police say the victim was one of three men attacked earlier in a fourth floor unit located in the 5800-block of North Winthrop Avenue, possibly as the result of a drug deal gone bad.
Two others, who also had their throats slit, died.
"They are new to this building. I think I saw one of them. It's really the short guy that I knew very well. I used to see him," said building resident Nnaemeka Ezakor.
Investigators learned of the crime as officers belonging to a gang crimes unit conducted surveillance in the area.
Around 5:30 p.m. Saturday is when police saw at least two suspects running from the building.
With officers in pursuit, the attackers fled north on Broadway in a pickup truck they used to ram a marked squad car.
A gun battle broke out wounding a 39-year-old officer in the leg.
"There are 20 police cars in the intersection. It's very frightening," said witness Marc Wright.
The chase continued to Greenview and Devon where the pickup's driver lost control and crashed.
One of the suspects -- 37-year-old Arturo Ibarra -- was shot and killed by police there.
"I guess he was shot before police pulled him out of the truck," said witness Brittany Rolling.
On Sunday afternoon, investigators say the suspects are a part of a "crew" allegedly tied other drug-related slayings over the last several months.
"They have no proclivity killing people if they want to, need to or if it's expedient for them," said Nicholas Roti with the Chicago Police Department.
Still, as expected, some building residents are shocked by the violence.
"What happened? Why did this happen here?" said building resident Harry Ezeocha.
Ald. Mary Ann Smith, 48th Ward, says as far as she knows, that building has not had any past problems.
"We are very proactive on crime. It is extremely unusual to have any kind of violent crime on the street but we're very anxious to get more details," Smith said.
Smith says she has worked hard to make sure there is enough affordable housing in her ward.
She says landlords are supposed to screen tenants with criminal pasts.
Smith is scheduling a community meeting Monday night with police to talk about Saturday night's crime.
Police say the suspects involved in Saturday night's murders and police chase may be wanted in several drug-related murders in different parts of the city.