The pair walked into CiCi's Pizza and gunned down officers Alyn Beck, 41, and Igor Soldo, 31.
One of the officers was able to fire back before he died, but it was unclear if he hit the suspects, Sheriff Doug Gillespie of Las Vegas Metro police said.
One of the gunmen yelled: "This is a revolution," but police said the motive behind the attack was still being investigated.
The suspects then fled to a nearby Walmart store, where they killed a person inside the shop and exchanged gunfire with police before killing themselves. The woman shot the man before killing herself, Sheriff Gillespie said. The suspects' names have not been released.
Officer Beck had been with the police department since 2001 and leaves a wife and three children.
Officer Soldo had been with the force since 2006 and has a wife and baby.
Eyewitness Pauline Pacheco was in Walmart when she saw the armed man and grabbed her father to escape. She said: "We saw the man walking. He was shouting, yelling bad words, and suddenly he had a gun. It was terrible."
Assistant Sheriff Kevin McMahill said the man yelled: "Everyone get out!" before shooting at Walmart.
Nevada governor Brian Sandoval said he was devastated by the murders of the two officers and an innocent bystander.
Las Vegas mayor Carolyn Goodman called the killings a "cruel act" and praised the officers for dedicating "their lives to protecting all of us in our community".
Walmart expressed its condolences and said the company was working with police on the investigation. Cici's Pizza said the company was deeply saddened by the shooting and would keep the restaurant closed until further notice.