Somdev, ranked 177th, lost 3-6 6-3 3-6 to his 18-year old opponent, whose father is a boxer and mother a tennis coach.
Somdev has not won a main draw singles match on ATP Tour since September 2014 when he had beaten China's Xin Gao at Shenzen Open.
He had a chance to change that stat as he led 3-1 in the opening set but lost five games on the trot to hand his rival a one-set lead. Somdev won the second, stretching it to a decider but dropped serve in the sixth game and could never comeback.
Somdev saved two break points in his first service game but a forehand error after a long rally put him down by another. He saved that too with a winner, set up by opening up the court and held for a 2-0 lead when Rublev's attempted drop shot fell short.
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Somdev earned a chance to go 3-0 up by placing a perfect backhand drop shot but could not cash in on as Rublev finally got on board.
Rublev sent down a cruising forehand winner to earn two set points and sealed it with a powerful overhead smash.
Somdev led 4-1 in the second set and sealed it comfortably but fizzled out in the decider.
Before a ball was hit, spectators stood to applaud
Muhammad Ali after an image of the boxing legend, who died Friday, appeared on the giant video screen high up on the Philippe Chatrier court.
The British star broke back to level before reeling off the next four games for a 4-1 lead as Djokovic's game quickly and unexpectedly unravelled.
Murray remained in charge, finding time to loudly berate a French television interviewer for climbing uninvited into his player's box overlooking the court.
Djokovic then argued with umpire Damien Dumusois for refusing to have a point replayed at 15-0 as Murray served for the first set. But the Serb was horribly out of sorts even before that spat with his 13 unforced errors proving fatal.
Djokovic misread the geometry on a dropshot which would have given him a double break in the fourth game but he was soon 4-1 to the good.
The top seed remained ruthlessly dialled-in, broke again for 5-1 and levelled the final when Murray dumped a service return into the net.
Djokovic, with the Paris crowd loudly on his side for the first time in four final appearances, broke for 2-1 in the third set which became 4-1 off a sublime running, backhand, cross-court drop-shot.
Djokovic kept his foot on Murray's throat, breaking in the first game of the fourth set as the second seed carried on a running argument with the umpire over the positioning of the overhead camera.
The Serb broke to love for 5-2 and history was just moments away. However, there was still time for a twist as he cracked when serving for the title before finally sealing the triumph after three hours on court.