Murray misses match point to continue jinx against De Minaur
The three-time Grand Slam champion appeared poised to finally clinch a first win over Australian De Minaur after a double-break in the deciding set, but slumped to a 7-6(5), 4-6, 7-5 loss.
Murray has still not won a match at Bercy Arena since lifting the title in 2016 en route to finishing as the year-end world number one.
The Briton saw three set points come and go before losing the first set in a tie-break, but bounced back to level the match and then take control.
But he twice failed to serve out the match, missing a match point in the 10th game.
De Minaur instead secured victory to set up a second-round tie with either Serbian lucky loser Dusan Lajovic or French wildcard Benjamin Bonzi.
Murray let slip two game points in the 12th and final game before being broken again, smashing his racquet in frustration when his exit was confirmed after three hours on court.
It was De Minaur's fourth win over Murray this year.
Elsewhere on the first day of the tournament, US Open semi-finalist Ben Shelton lost 7-6(4), 5-7, 6-3 to Alejandro Davidovich Fokina.
American 14th seed Frances Tiafoe lost 6-3, 6-4 to Alexander Bublik.
The defeat ended Tiafoe's slim hopes of reaching next month's ATP Finals in Turin.
Karen Khachanov, the 2018 champion, progressed with a 6-4, 6-4 win over Australia's Max Purcell.