* Tanker's escape from navy is huge blow to govt
* Cargo is first oil sale from rebels demanding autonomy
* Clashes between rebels, pro-govt militias reported
* Western powers worry Libya will slide into chaos (Recasts with parliament voting PM out of office)
By Ulf Laessing and Ayman al-Warfalli
TRIPOLI/ES SIDER, Libya, March 11 (Reuters) - Libya's parliament voted Prime Minister Ali Zeidan out of office on Tuesday after a tanker loaded with oil from a rebel-held port escaped the navy, officials said.
Zeidan, a liberal weakened for months by infighting with Islamists, will be temporarily replaced by Defence Minister Abdallah al-Thinni, parliament spokesman Omar Hmeidan told reporters.
The news deepens the turmoil in the North African country, a member of the OPEC oil producer group, where the government has struggled to impose order and rein in militias that helped oust Muammar Gaddafi in 2011 but now defy state authority.
Deputies said they had mounted a no-confidence vote after the tanker managed to load crude at Es Sider port and escaped the navy, which earlier claimed it had seized the ship.
Zeidan had told Reuters late on Monday in an interview the navy and allied militias had halted the tanker and were escorting it to a government-controlled port in western Libya.
He had for months been facing rising opposition from Islamists and the wider public, which blamed him for Libya's bumpy transition since the 2011 NATO-backed uprising.
The spectacular tanker escape was the tipping point.
"The government has been weakened for a time and we need a new personality," said al-Sharif al-Wafi, an independent lawmaker. A new prime minister will be elected by deputies within two weeks, he said.
On Saturday, Zeidan had said the navy would bomb the tanker if it tried to leave the port, one of three occupied by eastern rebels demanding a greater share of oil wealth and power.
But the ship had moved into international waters early on Tuesday morning after a brief firefight with government forces, port workers allied to the rebels and an oil official said.
"We escorted the tanker out of the port at 3 a.m.," said a rebel fighter at the harbour. "We came under fire from light arms (from the navy) but there were no casualties."
In another worrying sign for the Tripoli government, rebel gunmen blocked the gate to an airbase in Sirte, a city located close to Es Sider.
Residents reported clashes in the afternoon between pro-government forces and rebels in the coastal city.
In Tripoli and the western city of Misrata, armed young men could be seen gathering to join a government force, residents said.
Western powers worry the conflict might break up the vast country dominated by competing tribes and militias, all heavily armed.
The port rebels also demand autonomy for the east, which had been neglected under Gaddafi as he concentrated power and wealth in Tripoli as well as his home region of Sirte.
The rebels, who have seized three ports and partly control a fourth, said they had dispatched forces to central Libya to deal with any government attack.
Libya has been trying to rebuild its army since Gaddafi's ousting, but analysts say it is not yet a match for battle-hardened militias that fought in the eight-month uprising that toppled the dictator. (Reporting by Ayman al-Warfalli in Es Sider, and Feras Bosalum and Ulf Laessing in Tripoli; Editing by Dale Hudson)