Thompson has never won a Tour title, while Murray has 45, including three Grand Slams, to his credit.
After the event, he admitted that this is the biggest win in his career and something which he definitely didn't expect to achieve at this meeting.
The straight set loss for Murray saw Thompson winning 7-6 (7-4) 6-2.
The British No.1 had little time to adjust to the courts at the Edgbaston Priory Club after reaching the final of the Nottingham Open on Sunday.
More concerning for Murray is not only the continuation of his poor form but the fact he has lost potentially a week's worth of competitive matches on grass, with Wimbledon fast approaching.
"I'm trying to get myself going week by week". I just wanted to go out there and enjoy it.
"It's not ideal, but guys have in the past also gone in to Wimbledon having not won lots of matches".
"I'm very thankful she sleeps in the evenings - it's a good thing - but it does mean I don't get to see her quite as much".
"He played better than me. that's what happened", Murray said.
"I lost to Nicolas Mahut in 2012 and used the extra time to play a couple of exhibition matches, and then reached my first final at Wimbledon".
For all Murray's inadequacies, the Australian 23-year-old played brilliantly, dictating the points with his rasping forehand and showing an aggressive approach that his more established opponent was simply unable to match.
Thompson had been beaten here in qualifying but was offered a reprieve when Aljaz Bedene pulled out with a wrist injury and took full advantage against the home favourite.
Murray must now try to regain confidence in time for the defence of his title at Wimbledon, which starts on July 3.
Although Thompson had failed to win an ATP main-draw match throughout past year, he did reach the final of the Surbiton Challenger last week, and looked sharp as a result.
"I do feel he served well and got a lot of free points from his serve, but I also feel like I have made a lot of mistakes in the second set and gifted him a few points which I wouldn't normally do".
"But I was certainly feeling better in the build-up here than I was going into the French". It's a grass court so it's quick.
The first set moved into a tiebreak, where Murray had a mini break, but a costly double fault from the Briton completely switched the momentum of that tiebreak and gave Thompson a fighting chance.
Murray had been virtually untouchable at Queen's, winning the tournament a record five times, with three of those triumphs coming in the last four years.