He kept his head in the Monaco sunshine even after Murray, who ended up being broken seven times in a match with 13 service breaks, had romped to a 4-0 advantage with the loss of just three points.
Fresh from his shock last-16 defeat to Spaniard Albert Ramos-Vinolas at the Monte-Carlo Masters, the world number one will join the likes of reigning champion Rafael Nadal, Kei Nishikori, Dominic Thiem and David Goffin in Catalonia after accepting a wildcard entry. Though he has not played Murray in the past, the 24-year-old had started the season on clay, reaching the final stages in Buenos Aires and Rio de Janeiro and also finished as runner-up in Sao Paulo.
"I only started serving properly four, five days ago, so I knew it was going to take time but I didn't expect to start the match serving like like that".
While Murray and Wawrinka both suffered eliminations, Novak Djokovic was able to battle through in his match, eventually edging out Pablo Carreno Busta in three sets in just under two-and-a-half hours.
"I m disappointed. I feel like I had enough chances to win. I need to decide now whether I go and try to get matches or whether I try to get myself in better shape physically, put as much work in as I can".
Murray conceded only three points as he romped into a 4-0 lead in the decider but claycourt specialist Ramos reeled off four games in a row and then broke again at 5-5 before sealing victory on his serve when Murray netted a dropshot.
Defending champion Rafael Nadal registered a speedy victory over promising teenager Alexander Zverev, beating him 6-1 6-1 in one hour and eight minutes.
Ramos-Vinolas will now lock horns with fifth-seeded Croatian Marin Cilic for a place in semi-finals.
"My elbow felt pretty good".
Thursday in Monte Carlo, he was up 4-0 in the third set of a third-round match against Albert Ramos-Vinolas.
"That's an important part of my game - playing the correct way in terms of tactics, hitting the ball in the right spots", Murray said.
Muller, a top-30 player for the first time aged 33 and one of tennis' flourishing old guard, missed a chance to take the set at 5-3, and that gave Murray the spark he needed as he broke back to love.