Murray finally saw off Dimitrov 6-4, 6-7 (5-7), 6-3, 7-5 in a fluctuating match that lasted three and a half hours and finished after midnight in Melbourne yesterday.
The Scot, who faces home favourite Nick Kyrgios in the last eight tomorrow, showed signs of his grand slam-winning best but insisted he had been fortunate to avoid a fifth set.
“I think I got quite lucky at the end. A few net cords went my way. A lot of the games, even in the fourth set – the momentum was switching a few times,” he said.
“Grigor’s an unbelievable athlete and extremely quick around the court. He’s got fantastic hands as well. I’m just glad I managed to get through in the end.”
Murray, seeded sixth, trailed 5-2 in the fourth set before rattling off five successive games to exact revenge on the man who ended his Wimbledon defence last year.
Kyrgios, who shot to prominence by beating Rafael Nadal at that same tournament, delighted a vociferous crowd by overcoming Roger Federer’s conqueror Andreas Seppi in five sets.
The 19-year-old saved a match point before winning 5-7, 4-6, 6-3, 7-6 (7-5), 8-6 to become the first Australian to reach the quarter-finals for a decade.
Third seed Nadal allayed fitness concerns by sweeping past South African Kevin Anderson in straight sets, while seventh seed Tomas Berdych was similarly efficient against Bernard Tomic.
In the women’s draw, seventh seed Eugenie Bouchard survived a second-set wobble to defeat Romanian Irina-Camelia Begu and set up a last-eight meeting with second seed Maria Sharapova.
Canadian Bouchard looked to be cruising at a set and a break up but lost five games in succession before reasserting her superiority and triumphing 6-1, 5-7, 6-2.