fought back to claim his first victory at the to see the most British singles player wins in the opening round here since 1973.
The British No.1 had to survive an opening set barrage from his fellow left-hander Mattia Bellucci under the roof on Court Suzanne-Lenglen before winning 3-6 6-1 6-1 6-2 in two hours and 35 minutes.
Draper had lost both his previous matches here - and was among six British players to lose here in the first round last year.
But this time six players - Draper, Cam Norrie, Jacob Fearnley, Katie Boulter, Emma Raducanu and Sonay Kartal - have won in Paris. And it is the first time in the Open era that three British men and three British have all won first round matches here.
World No.5 Draper, who reached the final of the Madrid Masters, will play the winner of the night match between home favourite Gael Monfils and Bolivia's Hugo Dellien.
He said: "Bellucci came out and played really aggressively. He played some amazing shots. He caught me a little bit off guard. I'm really proud of the way I was able to turn the game on its head. I was more aggressive. Credit to Mattia. He played incredibly.
"It is not how you start, it is how you finish and I finished pretty well."
World No.68 Bellucci was also looking for his first ever Roland Garros win after losing on his debut here last here. And the Italian started superbly as he raced into a 5-1 lead in the first set by breaking the big Draper serve twice.
The British No.1 got back one break and had four break points at 5-3. But after also saving two set points, Bellucci set up a third with an inside out forehand winner which hit the sideline. And the Italian then cheekily produced an underarm serve before hitting a winner on the return.
But Draper then regrouped to win the next three sets - and took his first match point with a forehand winner down the line.
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