Salvatore Pizzolo, 37, and Michele Assente, 33, were carrying out a routine inspection of the vat at the plant in Priolo Gargalla, in the Sicilian province of Siracusa, when the accident happened.
One of the workers fell while trying to set up a small surveillance camera by the vat's edge, while the other died while trying to save him.
The men worked for the Siracusa-based engineering firm, Xifonia.
Trade unions reacted furiously, calling a strike at the plant on Thursday against the lack of stringent workplace safety measures.
“Two young lives have been cut short, it's intolerable,” said Mimmo Milazzo from the Italian Confederation of Trade Unions (Cisl), while denouncing the “chronic delays concerning measures for the safety of workers”.
“We need more investment, more controls, more prevention and more training on safety.”
Eni said in a statement on Wednesday that investigations were underway to establish the cause of the accident.
“The company expresses its deepest condolences to the families affected by this tragic accident,” it added.
The company has not suspended work at the plant.