In the clash on the Gaza border, the fighters shot dead the soldier and were in turn were killed by Israeli security personnel.
The resistance group Al-Aqsa Martyrs Brigades claimed responsibility for what it called the "martyrdom operation" at the Erez border crossing.
The two fighters killed were Ahmad Ashraf Zaqqut and Ayman Yousef Sahwein.
At least two other Israeli soldiers were wounded in the early morning clash between the fighters and the occupation soldiers, our correspondent reported.
Since a woman bomber from the Islamic resistance group Hamas killed four people at Erez last month, the Israeli military has stepped up supervision over some 3000 Palestinian workers who pass through the crossing every day.
The Israeli military sent home the Palestinian workers after the clash.
Witnesses said they heard firing in the area and saw troops searching a nearby sewage canal.
Palestinian security sources said the fighters were believed to have used the canal to enter the industrial zone.
In Biddo, Israeli troops shot dead
two 'apartheid wall' protesters
Civilians shot dead
In the second incident, the two Palestinian civilians were shot dead by Israeli troops during a demonstration against Israel's 'apartheid wall'.
The deaths of the two Palestinians in the village of Biddo, northwest of Jerusalem, were confirmed to AFP by Palestinian workers who witnessed the scene.
Muhammad Rayan, 25, was fatally hit by a bullet in his spine and Zakaria Eid, 28, was killed by a bullet in his chest, medics said.
Several other demonstrators were wounded during clashes with Israeli soldiers, they added.
Meanwhile, Israeli forces arrested 14 Palestinians early on Thursday in the West Bank cities of Nablus and Bethlehem, our correspondent reported.
The Israeli operations focused on Balata and Aida refugee camps and the towns lying to the south of Bethlehem city.