One of the damaged lines has been reconnected to Ukraine's electricity grid - but three are still down.
Crimea's two million people have been badly hit by widespread blackouts.
The repairs took place after talks with activists who have been blocking energy supplies to Crimea, which Russia annexed last year.
The Kakhovskyy-Titan power line was reconnected overnight "with agreement from activists involved in the energy and food blockade of Crimea," said authorities in Ukraine's southern Kherson region, quoted by Interfax news agency.
The Russian energy ministry also confirmed that the supply to Crimea had been resumed.
Unknown attackers damaged the four pylons on 22 November. Anti-Russian activists were blamed.
Crimean Tatar activists have been denying repair workers access to the damaged power lines.
Ukraine's state energy company, Ukrenergo, has said the damage was caused by "shelling or the use of explosive devices".
The loss of power to Crimea - causing widespread blackouts - highlighted the peninsula's reliance on electricity from Ukraine.
The four lines are the only sources of electricity for Crimea, so when they came down the territory was plunged into darkness, according to the BBC's David Stern in southern Ukraine.
Schools were closed and a state of emergency was declared.
The incident also sparked a reduction of coal supplies to Ukraine from Russia and from the pro-Russian rebel-held eastern Ukraine.
Russia has begun building an undersea cable to Crimea, to bypass Ukraine.
Ukraine says it has restored part of the electricity supply to Crimea, more than two weeks after power lines to the territory were blown up.