The men, aged 30 and 45, were rescued from the Trishuli 3A hydropower tunnel, the Nepali army said on Friday.
They were named as Sanjay Sah, a mechanical foreman, and Kabir Maharjan, a mechanical supervisor, Energy Minister Biraj Bhakta Shrestha's office said in a statement.
Both men were flown to a military hospital in the capital Kathmandu.
One of the rescued men was suffering from mild hypothermia and had been able to communicate clearly, an army spokesman said, while the condition of the other man was initially unclear.
Videos from Nepalese media showed one of the survivors, covered in mud, being pulled out of an opened shaft.
He had been working in the plant's control room as the flood wave approached, a representative of the Nepalese army quoted Sah, as saying.
Sah said he had warned dozens of colleagues about a "serious dam breach" and shouted at them to get to safety immediately.
"But while I was trying to save everyone, I was running out of time. I did not manage to get out myself in time," Sah was quoted as saying.
More than a week after the disaster, rescuers from the army and police had stepped up their rescue efforts after hearing voices, lawmaker Shri Ram Neupane was quoted by the newspaper The Kathmandu Post as saying.
"Don't panic, we are here to rescue you," the rescue team were reported as shouting. An "OK" came back in reply from the shaft.
The flooding, which originated in a glacial region of the Himalayas, devastated numerous hydropower facilities, some of which were still under construction.
Hundreds of workers remain missing and are believed to be trapped in tunnel systems at the plants.
The tunnels are primarily used to transport water through mountainous terrain in order to make more effective use of differences in elevation to generate power.
Teams of specialists from India, China and South Korea were taking part in the search and rescue operations in co-operation with the Nepali Army, the Foreign Ministry in Kathmandu said.
According to official figures released on Friday, the death toll in Nepal had risen to 1290, with almost 4800 people still missing, including 601 foreign nationals.
The death toll on the Tibetan side of the border rose to 31 on Friday, an increase of 10 since the previous tally, according to Chinese state media.
It was not clear whether they were Chinese or foreign nationals. Some 531 people were reported missing.
The European Commission said that 82 tonnes of essential relief supplies from EU stocks were flown into Nepal on Friday.
Separately, Germany, Luxembourg, Latvia and Norway were sending protective equipment, medical supplies and emergency power equipment.
Australian disaster response specialists left for Nepal on Friday to join the search for survivors, as the Albanese government expressed "serious concerns" for the welfare of its missing citizens.
Authorities in Canberra on Friday confirmed two people had made contact overnight, bringing the number of missing Australians to 36.
with Reuters, AP, AAP
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