But Hurkacz, who defeated Roger Federer to reach the Wimbledon semi-finals this summer, proved a step too far, the Pole prevailing 7-6 (4) 6-3.
Murray was obviously frustrated not to win a first set where he was the better player, missing three opportunities to break in the eighth game.
And Hurkacz took advantage in the tie-break before raising his level in the second set. He broke Murray’s serve in the fourth game and held off an attempted fightback from his opponent to clinch victory.
Murray said: “It was frustrating to lose, obviously. I had chances again and didn’t take them.
“I’m not saying I deserved to win the second set, he served extremely well and I played one loose service game. But in the first set I had chances and I should have taken them, didn’t, and against players who are that good, you don’t get loads. Disappointing.”
This week was a small step forward for the 34-year-old but he still remains outside the top 100 and is in a hurry to climb the rankings to avoid the sort of draw that saw him play Stefanos Tsitsipas in the opening round of the US Open.
“I think I played better this week than I did in Cincinnati and Winston-Salem, for example,” said Murray.
“I did play a pretty good match at the US Open. But I’m not that interested in playing well and losing. I want to be winning these matches. But the consistency this week was better than it was over in the States.
“My goal’s not to get in the top 100. I would want to get back in the top 10 would be more something that would motivate me in terms of a goal. Winning tournaments and getting up towards the top of the rankings is motivating to me.
“Hopefully between now and the end of the year I can play a lot of matches and try to do better than this week.”
Hurkacz will take on German Peter Gojowczyk in the semi-finals while Murray is due to play in next week’s ATP tournament in San Diego.