At least nine were also wounded, according to the source.
The militant groups claimed responsibility, calling the attacks a joint "self-sacrifice operation" in a message posted on the Hamas Web site.
Israel is on heightened alert for an attack during the holiday of Purim that begins at sundown on Saturday.
One assailant entered the Israeli side of the crossing terminal in a jeep altered to look like an Israeli military vehicle, an army spokeswoman said. The man fired on soldiers, who shot back, killing him.
The second attacker blew himself up inside a vehicle on the Palestinian side of the crossing point. The blast destroyed a car and body parts were strewn around the wreckage.
Two Palestinian policemen were killed by the blast, the army said.
Palestinian hospital officials said the two died of gunshot wounds. Nine other people also suffered gunshot wounds.
Witnesses heard shooting after the explosion.
"The sound of the explosion was huge and powerful, followed by intense machine gun fire from the Israeli army outpost," taxi driver Ali al-Basyouni said.
Also Saturday, a 19-year-old Palestinian policeman was killed by Israeli army fire in a West Bank refugee camp.
The military said soldiers opened fire after the man drew a gun.
But Palestinian witnesses said he was killed during a clash between soldiers and dozens of stone throwers, including many children on their way to school.
The incident took place in the Tulkarem refugee camp during a routine military patrol, the army said.
The dead man was identified as Taher Abu Sariyeh, a member of the Palestinian security forces. Abu Sariyeh was in uniform at the time of his death and carried a weapon, hospital officials said.
The Associated Press contributed to this report.