The Briton, who beat big-serving South African Kevin Anderson on Monday, has enjoyed a smooth run into the second week, playing within himself to reach the quarter-finals without dropping a set.
But the 23-year-old Dimitrov, on a nine-match grasscourt winning streak, provides an extra challenge for the twice grand slam champion.
“It’s a step up…the guys in the quarter-finals are going to be playing top tennis. He obviously won at Queen’s Club a couple of weeks ago. He likes grass courts,” Murray told reporters.
“He’s starting to come into his prime. He’s won a lot of matches this year. It’ll be a hard match for me.”
Murray neutralised Anderson to win 6-4 6-3 7-6 (6) in a match that started in the open and ended under the Centre Court roof.
The 27-year-old Scot returned sharply and drew the 2.03-metre (6-foot-8) Anderson into rallies to impose his game on the Wimbledon grass where he is on a run of 17 successive victories.
Anderson, a career-high 18th in the world, broke serve only once, after rain forced a roof-closing pause with Murray 3-0 up in the second set.
He upped his game in the third set to force a tense tiebreak and even had a set point before the Scot won three points in a row to reach his seventh successive Wimbledon quarter-finals.
“I started off a bit tentative when we came back out,” said Murray. “When it was outdoors I played very well and was in a good position but when we came indoors he was striking the ball better.
“There’s a big difference between playing indoors and outdoors. It changes the way the court plays…but I still did well. I still created loads of chances, a lot of opportunities,” Murray said.
Anderson had nothing but praise for Murray.
“Even on the return of serve I felt like he reads it really well, the 28-year-old said.
“He moves very well and I felt a lot of the times he was going to where I was hitting the ball which made it tough.
“That’s a big part of his game. Especially on the grass I think that’s a big contributor to why he’s had so much success on this surface.”
The champion started in relaxed style, breaking Anderson’s booming serve in the third game and wrapping up the opening set in 43 minutes. Looking supremely comfortable on the turf where he also won Olympic gold in 2012, Murray broke the South African twice early in the second set but the rain started to fall and organisers decided to close the roof. The 2012 U.S. Open champion, who always prefers playing in the elements, dropped his serve and two games later wobbled again to offer Anderson another break point. Murray saved it but his opponent found a new confidence that he took into the third set, firing his 76th ace of the tournament to earn set point. The ice-cool Murray replied with a big serve, forced an error to earn match point and produced a backhand winner to progress to the last eight to the delight of a noisy crowd. “When you play in front of a big crowd like this you raise your intensity and it helps you in a big way,” he added. Anderson said the atmosphere was electric.
“I didn’t feel put off by the crowd at all. It was really enjoyable playing out there,” he explained.
(Editing by Tony Jimenez)