Last updated on .From the section Tennis
The British number one beat the Irishman in the final.
It is the third title for the 26 year old, who won at Indian Wells and Los Cabos in the last two years.
Norrie failed to take any of his five break points but won both sets of a hard-fought contest on a tie-break.
The last left hander to win the tournament was in 2004.
Norrie rose from 74 to 13 after losing last year's semi-final.
Norrie won in one hour and 51 minutes and said that he enjoyed his time on the court.
You are moving great. He told the world number 20 that he was going to break into the top 10.