Lawmakers changed voting procedures Friday after the flamboyant pro-Western Tymoshenko narrowly failed by a single vote to get backing for her appointment first time on December 11.
Two votes were held, with Tymoshenko both times receiving 225 votes, one short of the 226 required. The coalition blamed technical malfunctions.
"Most MPs met the Party of Regions halfway and decided to consider the premier's candidacy Tuesday," Rada Speaker Arseniy Yatsenyuk said.
A total of 274 MPs voted for the decision Friday with 226 required.
Yatsenyuk said pro-Western lawmakers did not trust the electronic voting system and would vote by a show of hands.
On Wednesday, the coalition's opponents, the Party of Regions led by acting Prime Minister Viktor Yanukovych, blocked a new vote on Tymoshenko, who briefly held the post of premier in 2005, by obstructing the rostrum.
Tymoshenko's coalition won a total of 227 seats in September's parliamentary elections, one vote above the 226 votes required to form a majority in the 450-seat Supreme Rada.
