Wawrinka has struggled to return to peak form since suffering a left knee injury last yeat that required two operations and wiped out the second half of the Swiss star's season.
Still hampered by the problem this term, Wawrinka was sidelined again for three months in between a second round exit at the Australian Open and a first round loss in the French Open.
The 33-year-old arrived in west London having lost six of his last seven ATP Tour matches and, given grass has never been Wawrinka's favourite surface, he might have feared more misery at the pre-Wimbledon event.
But the three-time Grand Slam champion had an obliging opponent in wild card entry Norrie.
Wawrinka hardly had to break sweat to see off Norrie and next faces former Queen's winner Sam Querrey of the United States, who beat British wild card and ATP Tour debutant Jay Clarke 6-3, 6-3.
"Mentally it's tough when you see how far you are and how long it will take. Still now, it's not easy," Wawrinka said of his injury woes.
"It takes time to get where you want to be. I need to be really patient with myself, to accept less in a way, because, when you win Grand Slams, I always expect so much from myself."