Though Zverev broke Norrie's opening serve in the first set, the Brit matched his opponent to force a tie-breaker. However Zverev dominated the tie-breaker, claiming every point.
Zverev has enjoyed great form across the tournament, having yet to drop a set and hitting 10 aces compared to Norrie's two over the course of the match.
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The German never appeared to be under much pressure, and made no errors, looking solid at the baseline to deny Norrie a second ATP tour final.
Zverev said: "It was very tough. It was pretty windy out here, not easy conditions, and his game actually I think fits the wind quite well, so it was not easy.
"I'm just happy to be through. At this stage, you've got to win matches, no matter how. I'm just happy to be in the final."
Zverev will face Kyrgios in the final, who beat John Isner 7-5 5-7 7-6(7).
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