(Adds economy minister staying on, background of new prime minister)

LIMA, April 2 (Reuters) - Peru's president named Defense Minister Pedro Cateriano as prime minister on Thursday, replacing Ana Jara, who was thrown out of office by Congress earlier this week amid allegations of corruption.

A survivor of the cabinet shakeup was Alonso Segura, Peru's market-friendly economy minister. His task this year is to attract investment to the country's key mining sector as a way of arresting the country's economic slowdown.

Cateriano, a 56-year-old lawyer, had been defense minister for almost three years. Known for taking a hard-line with the opposition, his becoming prime minister may do little to improve President Ollanta Humala's already difficult relationship with Peru's 130-member, unicameral Congress.

His predecessor, Jara, lost a confidence vote in Congress following allegations of spying on her opponents. It was the latest in a series of political blows absorbed in recent months by Humala, whose approval rating has hovered around 25 percent this year, according to polling firm Ipsos Peru.

(Reporting by Marco Aquino; Writing by Hugh Bronstein; Editing by Lisa Shumaker)