Murray recorded his first win after almost a year out with a hip injury, beating three-time grand slam champion Wawrinka 6-1 6-3 in just 77 minutes at Eastbourne.
The Scot made his long-awaited comeback last week in a three-set defeat to Nick Kyrgios at Queen’s Club but showed further signs that he is getting back to full fitness on the south coast.
• READ MORE - Andy Murray bags his first victory in almost a year
With Wimbledon set to start next week, the two-time winner at the All England Club has refused to commit himself as he continues to work his way back and Judy Murray was not reading too much into the win.
“I think he did really well yesterday, but this is about him just dipping his toe back in the water and seeing how his body holds up,” she said at the inaugural UK Coaching conference in Edinburgh.
“It was great for him to have a win.”
With Murray now through to the second round at Eastbourne - where he will face fellow Briton Kyle Edmund on Wednesday - he could yet suffer an adverse reaction to the strains of being back on court.
He admitted to experiencing soreness and stiffness after the loss to Kygrios and any further problems could see him pull out of Wimbledon next week, but Judy Murray says it is vital he gets match time under his belt if he is to get back to his best.
“The goal was always to try and play the grass court season and at some point you have to dip your toe back in the water to see where you are at,” she said.
“Any athlete who has been out for a long time will tell you the same thing, you have to build up your physical fitness and your match fitness and you can only build that up by playing matches.
“I think for him it is about seeing how he is during the match, and how he is after the match.
“That is what tennis will demand of you; if you are playing in a tournament that lasts for a week and you get to the final, you have to play five matches in seven days.
“If you play a grand slam, you’re playing seven matches across 13 days and the best of five sets, so you have to test yourself and see where you are at.
“I think he had a good match at Queen’s last week and had a good match yesterday with Stan, so it’s just baby steps.”
• The inaugural UK Coaching Conference is taking place at Oriam in Edinburgh from Tuesday 26 - Wednesday 27 June, focusing on the next generation. For more information on #GreatCoaching, visit www.ukcoaching.org.