Defending champion Murray had been expected to get the better of his Bulgarian opponent, but the number 11 seed came out on top thanks to a 6-1 7-6(4) 6-2 win on Centre Court to advance through to the semi-finals.
Speaking after his victory, 23-year-old Dimitrov told BBC Sport: "I am excited and just happy I got through that match in straight sets. It's never easy coming to play Andy in front of a home crowd and I am just fortunate and happy.
"As soon as we started warming up I sensed his game was not at the highest level and I was feeling good. I held my ground through and the tie break was crucial. I went into the third set very positive. Today was one of those days when I was pretty steady for the whole match and came out the winner."
Dimitrov has never previously gone beyond the second round at SW19.