Murray could not overcome Rublev in the exhibition event following a strong week on route in the Middle East that saw him beat compatriot Daniel Evans and Rafael Nadal — his first match against the Spaniard since the Madrid Open in 2016.
Rublev took control midway through the first set with a break of serve in the fifth game on the way to a decisive 1-0 lead.
The Russian looked to be cruising to a victory when he broke Murray in the opening game of the second set, but the Scot fought back, pushing the world No. 5 to a tie break.
However, Rublev outlasted Murray to claim the tie break 7-2 and seal the match.
Murray’s attention now turns to Australia, where he will take part in the season’s opening major for the first time since 2018 in January.
Earlier on Saturday, Nadal continued his comeback after sustaining a foot injury in August in the third-place playoff against Canada’s Denis Shapovalov, but the Spaniard suffered a 6-7(4), 6-3, 10-6 defeat.