Rovers were denied a grandstand finish when Mawson got his fingertips to Muirhead's goalbound effort, before Carlton had the final say from close range.
Paul Barnes' volley, Simon Marples' free-kick and David Morley's header all forced home keeper Craig Mawson into action in the minutes after the re-start.
Mrs Mawson was recognised earlier this year for her work in reuniting Guernsey evacuees with people in the north of England who had housed them during WWII.
She has benefited from access to more than 150 photographs taken by Endurance crew-member Frank Hurley, an Australian postcard photographer who had previously visited Antarctica with Douglas Mawson in 1911.
"The garden is considered to be the best Edwardian garden in Wales and was the result of a creative collaboration between Thomas Hayton Mawson, one of the most influential garden designers of the early 20th Century, and Reginald Cory, " she said.