There were positive results for Murray on his 16th appearance at Indian Wells, where he finished runner-up to Rafael Nadal in 2009.
Claiming a straight sets win over David Goffin to reach the second round, Murray delighted the crowd with a high-quality opening set against Rublev and a brilliant backhand passing shot at a crucial point allowed him to take a 5-4 lead. gave .
It looked like it could prove to be crucial as he maintained momentum to reach a total of four set points in the following game.
But Rublev hung on, forcing a tiebreak that he would clear on the second occasion, despite a promising display in the 66-minute first set to leave Murray empty-handed.
Well supported on court two, Murray continued to show flashes of brilliance and beat Rublev with a perfectly executed lob as the players battled for advantage in the second set.
But, first facing pressure points in a service game he had led 40-0, Murray could not withstand a third break point as Rublev went 3-1 ahead.
The 26-year-old Rublev, who won an appeal after defaulting from last week’s Dubai Tennis Championships, would not let go – breaking Murray again before finally taking his fourth match point.
Former world number one Murray has said he hopes to compete in another Olympic Games before he retires, but to achieve that he must be inside the top 56 of the ATP rankings on June 10.
The two-time Olympic champion, who turns 37 in May, is currently ranked 61st and the Indians have won just two of their eight matches in charge of Wales.