There were positives to take for Murray on his 16th appearance at Indian Wells, where he finished runner-up to Rafael Nadal in 2009.
Having claimed a straight-set win over David Goffin to reach the second round, Murray delighted the crowd in a high-quality opening set against Rublev and a stunning backhand passing shot on a crucial point allowed him to hold serve for a 5-4 lead.
It looked as though that may prove pivotal as he maintained momentum to reach a total of four set points in the following game.
But Rublev hung on, forcing a tie-break which he would clinch at the second opportunity, to leave Murray empty-handed despite a promising display in a 66-minute first set.
Well supported on court two, Murray continued to display flashes of brilliance and beat Rublev with a perfectly executed lob as the players fought for an advantage in the second set.
But, first to face pressure points in a service game he had led 40-0, Murray could not withstand a third break point as Rublev moved 3-1 ahead.
The 26-year-old Rublev, who won an appeal after being defaulted from last week’s Dubai Tennis Championships, would not let up from there – breaking Murray again before eventually taking his fourth match point.
Former world number one Murray has said he hopes to compete at another Olympic Games before he retires, but to achieve that he must be inside the top 56 of the ATP rankings on 10 June.
The two-time Olympic champion, who turns 37 in May, is currently ranked 61st and won just two of his eight matches in the lead-up to Indian Wells.
