Popyrin, competing in his first semi-final since winning his second career title in Croatia last July, looked in the driving seat for much of the opening set at Doha's Khalifa International Tennis and Squash Complex but eventually succumbed in the breaker before going down 7-6 (14-12) 6-2.
The centrepiece of an absorbing contest on Friday was a terrific battle in the breaker in which Popyrin held three set points and No.2 seed Khachanov had five of his own before finally prevailing after a 65-minute stanza.
After the Russian had fought back from 4-2 down in the opening set to level up and then set up the tiebreak, things had initially looked forlorn for Popyrin as he quickly went 4-0 down.
But Popyrin fought back magnificently, even saving the set with a daring second serve that caught the line, but there proved one gamble too many when he also chalked up a double fault to give Khachanov the fourth of his set points.
Again, the Australian responded by going back on the attack to save the day again, but Khachanov, such a tough competitor, delivered typical aggression of his own when he finally forced Popyrin, on the retreat on his own serve, to hit low into the net and surrender the set on the 26th point.
It was always going to be a long way back for the 24-year-old after that crushing blow and there was almost a sense of inevitability about the world No.17 taking control with a break in the third and seventh games of the second set as he went on to win in just over an hour and three-quarters.
It means world No.46 Popyrin will stay as No.3 in the new Australian men's rankings when they're released next week, still behind Jordan Thompson and No.1 Alex de Minaur, but he'll potentially also be enjoying a new career-high position in the top 40.
