Evans, who performed well at the ATP Cup earlier in January as Great Britain reached the knock-out stage, lost out 6-4 3-6 6-3 to the Russian who himself won for the sixth time in 2020 and made it 10 in a row stretching back to last year. Rublev also picked up the ATP Cup in Doha last weekend.
Evans will be seeded 29 at the Australian Open, the first Grand Slam of the season which gets under way on 20 January, following the withdrawal of local hope Alex de Minaur through injury.
The 29-year-old was seeded in a Grand Slam for the first time in his career at Thursday's draw, and will face-off against American world No.132 Mackenzie McDonald in the first round. The draw could see him come up against Novak Djokovic in the third round.
British number three Kyle Edmund also fell at the quarter-final of his last Open warm-up tournament, going out 7-6 (7-5) 7-6 (7-5) to John Isner in the ASB Classic in Auckland.
Isner's serve was a pivotal factor in the win, scoring 25 aces during the match and enjoying a first serve percentage of 75%.