BRUSSELS, Oct 3 (Reuters) - Margrethe Vestager has won the European Parliament's backing to become the European Union's new competition commissioner following her confirmation hearing, lawmakers said on Friday.

The Danish liberal, a free-trade advocating economy minister at home until nominated to the incoming European Commission post, will be responsible for high profile cases such as Google .

Vestager, 46, is set to take up her post from Nov. 1 in the new European Commission but under EU rules, all nominees for the EU executive must be approved before the Commission can begin its term.

(Reporting by Robin Emmott; editing by Philip Blenkinsop)