The building was stormed by rebel forces, which had snipers and rocket launchers in nearby apartments. Five rebels were killed and eight were injured, spokesman Oleg Slobodyan of the Ukrainian border service said, adding seven guards were injured.
The separatists' action appeared to be designed to seize control of the closed Ukraine-Russia border and bring in supplies and additional forces. The border guards are among the few effective government representatives in the region, since army and security troops have essentially abandoned the government cause or joined the rebels, but are not skilled in combat.
"We're doing the best we can, but our mission was never intended to be one that repelled large armed attacks," Slobodyan said.
The Russian news agency Itar-Tass reported a Ukrainian fighter plane was sent to protect the building, but Slobodyan said it did not fire into the neighborhood.
The incident highlights the problematic nature of President-elect Petro Poroshenko's promise to crush the rebellion in eastern Ukraine. Luhansk and neighboring Donetsk provinces are, for the most part, under rebel control, and the border between Russia and Luhansk is relatively weakly patrolled.
In a separate incident, armed men entered the offices of two Donetsk newspapers and abducted their editors. It was unclear where they two men, who edited the newspapers Donbas and Vecherny Donetsk, were taken.