It has been a superb season so far for Draper, claiming a maiden Masters 1000 title at Indian Wells, improving his fitness and finding another level of power behind his shots.
But he was the weaker player in the first set, capable of out-hitting Moutet but too often dragged out of position.
He hit 15 unforced errors to four from Moutet, who sealed the opening set with an emphatic ace.
Draper jogged to his chair at the end of the set to try and find some energy, often shouting “Jack, come on!” after an error and berating himself.
He steadied himself well after the video review, requested by Moutet at 4-3 in the second set. The video showed Draper had got his racquet head to the ball, with the frame causing the ball to bobble awkwardly and draw the error out of Moutet’s forehand in response.
Moutet briefly argued with the umpire and, perhaps distracted, played a poor next service game to be broken and allow Draper to serve for the set.
The Frenchman looked to have recovered when he broke Draper back to love, but Draper kept up the pressure and forced a deciding set on a long lob, with the Briton cupping his hand to his ear, urging more support.
Both served well in the third set but fatigue again played a part, with Moutet forced to take a medical timeout at 4-3 down after struggling with his thigh.
Draper promptly broke in the next game and then served out the match, closing it out with a well-timed serve and volley.
“I had a word with myself after the first set – I needed to really knuckle down and focus and I knew his level wasn’t really going to drop,” Draper added.
“I came out in the second set and fought for every point and found a way in the end to pick up my level.”
