Abraham Ozeri, an 86-year-old Jerusalem resident, died of his wounds shortly after the terror attack. The policeman, 30, was taken for treatment at the Hadassah Hospital in Ein Kerem, where his condition was classified as serious.
The attacker, 20-year-old Mohammed al-Badan, was shot and disarmed during the attack.
The Palestinian militant group Hamas added that the terror attack came as a direct response to Israeli moves to make Jerusalem more Jewish.
Police spokesman Micky Rosenfeld said two police officers on patrol in Gilo had stopped an Arab for questioning on the street when he pulled out a knife and stabbed one of them.
"The [wounded] policeman fired at the terrorist, but he continued to attack and stabbed a 86-year-old passerby, before he was apprehended," Rosenfeld said.
A civilian, Yoav Mizrahi, and a municipal inspector, Yehoshua Ben Nun, who were in the area gave chase, seizing the Palestinian some two hundred meters away from the site of the stabbing.
Mizrahi said: "I succeeded in grabbing hold of his back, and with the municipal inspector who was in the area, we held him and called on civilians to phone the police and Magen David Adom [emergency services]. I put my leg on him and pointed a gun at him until the police arrived."
There was no immediate claim of responsibility for the stabbing.
Magen David Adom, revising its information that the Palestinian was killed, said he sustained moderate wounds.
IDF raids assailant's village
The Israel Defense Forces later searched the West Bank home of the attacker in the village of Tekoa, near Bethlehem. Witnesses said two of al-Badan's friends were taken away in military jeeps.
Witnesses said about 100 local teenagers hurled rocks at the soldiers, who responded with tear gas and rubber bullets. Palestinian medics said three Palestinians were lightly injured. The army said a soldier was also lightly wounded in the clash, but it gave no further details of the operation.
Security establishment sources said the police officers' alertness had likely foiled an attack on one of the educational institutions in the area.
On September 22, a Palestinian plowed his car into a group of soldiers at a busy intersection, injuring 13 before he was shot dead.
In two incidents in July, Palestinians carried out attacks on city streets using heavy construction machinery, killing three people and wounding several others.
About two months ago, an Israel Defense Forces soldier was lightly to moderately wounded when he was stabbed by a Palestinian near the Almog Junction north of the Dead Sea.