BANGKOK — Political neophyte Paetongtarn Shinawatra won the backing of parliament to become Thailand’s youngest prime minister on Friday, only a day after she was thrust into the spotlight amid an unrelenting power struggle between the warring elites.

The 37-year-old daughter of divisive political heavyweight Thaksin Shinawatra passed the required threshold of 51% of votes and now faces a baptism of fire, just two days after ally Srettha Thavisin was dismissed as premier by a…