The British number one arrived in Paris full of confidence, winning the Lyon Open two days earlier for his first ATP Tour title on clay.
There was no sign of any hangover from that at Roland Garros, against Frenchman Guinard. Norrie edged a tight first set before breezing through the second and wrapping up victory with a bagel in a 7-5 6-2 6-0 win.
For all Norrie has had an incredibly impressive 12 months, he is yet to bring that consistency to tennis’ four biggest tournaments and has never made it past the third round of a Grand Slam.
The world number 11, who fears Wimbledon will be reduced to an exhibition event after it was stripped of ranking points, will face Jason Kubler in the next round. The Australian came through three tie-breaks to beat Denis Kudla and already has plenty of matches under his belt, winning three qualifiers to reach the main draw.
“I have to be patient with the clay,” Norrie said after the match.
“When I’m playing well I can love it, but when I’m not I have moments where I’m not.
“It feels really good to win today. It would be the first time I’ve made the second week of a Slam and I’d like to tick that box.”
Roland Garros has been a miserable venue for Dan Evans in the past - he had never previously won a main draw match in Paris. That’s changed now though, and on his 32nd birthday too, as he battled past Francisco Cerundolo 7-6 6-4 6-4.
It threatened to be a nervy third set for Evans, despite the fact he moved 3-0 up in it and seemingly in complete control. Cerundolo responded with two breaks of his own to level it up, but he could not then hold serve as the pair exchanged breaks once more.
Evans made it seven breaks in nine games in the set to move 5-4 up and then kept his nerve to serve it out and book his place in the second round. He will face either Mikael Ymer or James Duckworth in the third round.