Murray was coasting at two sets up but squandered four match points in the third, which Robert eventually won on a tie-break. The Scot took his frustration out by breaking his racquet.
It took two hours and 21 minutes but Murray was finally though to his 12th grand slam quarter-final in a row at tournaments he has contested.
Murray's broken racquet lays beside his bag
Robert stayed on court to soak up some deserved applause as a relieved Murray celebrated surviving his first hiccup.
Murray eventually prevailed in four sets on Monday