World No.5 Rublev secured a 6-4 7-6 (7-2) victory over the three-time grand slam champion in the final in Abu Dhabi.
Murray had beaten Rafael Nadal in the exhibition event, but was unable to end the year on a high note.
Rublev claimed the only break of a tight first set and dominated a second-set tie-break after Murray had fought back from failing to hold in the opening game.
Murray had been given a way back into the contest when Rublev threw in three double faults in the eighth game of the second set to be pegged back at 4-4, but was unable to force a decider.
Nadal suffered another loss as he works his way back from injury, with Denis Shapovalov coming from a set down to beat the legendary Spaniard 6-7 (4-7) 6-3 10-6.