There were some positives for Murray in his 16th appearance in Indian Wells, where he finished runner-up to Rafael Nadal in 2009.
After winning in straight sets over David Goffin to reach the second round, Murray delighted the crowd with a quality opening set against Rublev and a stunning backhand winner on a crucial point allowed him to hold serve for a 5-4 lead. .
And that looked like it could be pivotal as he kept the momentum going to a consistent four-point total in the next game.
But Rublev held out and imposed a tie-break on the second chance, leaving Murray empty-handed despite a promising performance in the first set, which lasted 66 minutes.
Murray, who was well supported on court two, continued to show flashes of brilliance, beating Rublev with a stunning volley as the players battled for advantage in the second set.
But, first, Murray faced pressure points in his service game as he led 40-0, and Murray was unable to hold on a third break point as Rublev took a 3-1 lead.
The 26-year-old Rublev, who received an appeal after missing the Dubai Tennis Championships last week, did not back down, as he broke Murray again before finally getting a fourth match point.
Murray, a former world No. 1, said he hopes to compete in another Olympics before retiring, but to do so he must be among the top 56 players in the ATP World Rankings on June 10.
The two-time Olympic champion, who turns 37 in May, is currently ranked 61st and has won just two of his eight matches in the lead-up to Indian Wells.
