WASHINGTON, Nov 5 (Reuters) - Kansas Republican Governor Sam Brownback has won re-election, NBC projected, beating Democrat Paul Davis in the historically Republican state despite a bruising campaign that focused on the fiscal problems that followed Mr Brownback's tax cuts.

Mr Brownback, 58, has been Kansas governor since 2011 and was previously a United States senator.

But his conservative economic policies prompted some moderate Republicans in the state to endorse Mr Davis, 42, Democratic leader in the state's House of Representatives.