The US Open champion, a winner at Queen's in 2009 and 2011, saw off Germany's Benjamin Becker to set up a mouthwatering last-four showdown with Jo-Wilfried Tsonga, but the Scot did not have everything his own way during his 6-4 7-6 (7/4) victory.
Becker broke twice in the second set to prevent Murray coasting to an easy win but the Olympic champion showed resilience to advance after dominating the tie-break, before revealing he was still struggling to find his top level on a consistent basis.
"All the matches this week are going to be tough because I haven't played a match for a month," he said.
"They're going to be tough, and there's going to be moments in the matches where your level drops a little bit. That's happened in the last couple of matches.
"So, with playing matches and getting match tight, I'll avoid those slip-ups, but it's important to go through them and come out the other side of them with a win, and I managed to do that the last couple of days.
"Ben made the final in Nottingham last week and he's come through three matches here. He's played a lot of tennis on the grass, and he started playing a lot better towards the end of the second set when I played a poor game at 2 1.
"That just comes with playing matches and also the first week on the grass, as well. All of the guys have had dips in matches and in sets. It happens."
After playing twice on Wednesday to secure safe passage into the quarter-finals with wins over Nicolas Mahut and Marinko Matosevic, Murray's back injury would have been feeling the strain.
But the 26-year-old revealed he is reaping the benefit of making the tough decision to sit out the French Open earlier this month.
"My back's been very good, the best it's been for a while," he said.
"Obviously when you start feeling things, that tends to be when you hold back but this week that has not been the case."
Murray's semi-final against world number seven Tsonga will be second on centre-court tomorrow, following the clash between defending champion Marin Cilic and four-time winner Lleyton Hewitt.
The 32-year-old Hewitt has been in great form throughout the week and will be fancied by many to collect his fifth Queen's title - and a first since 2006.
Murray has been impressed by the Australian's performances.
He said: "I saw his match today with (third seed Juan Martin) Del Potro, and he played very well.
"I practiced with him a few times the week before the tournament as he got here early from the French Open. He's obviously spent some time on the grass and he loves it here. He has got a great record here.
"He still competes incredibly well, and it is no surprise to see him causing upsets."
In the doubles, Jamie Murray and John Peers were beaten by the top-ranked American brothers Mike and Bob Bryan 7-6 (7/5) 6-7 (9/11) 11-9, whilst the Indian duo of Mahesh Bhupathi and Rohan Bopanna were too strong for British pair Colin Fleming and Jonny Marray, winning 7-6 (7/5) 4-6 10-4.