The player, who is now ranked 49th in the world, outplayed Murray, who has been in poor form of late and only recently lost in the semi-finals in the Godo Tournament in Barcelona.
Rising Croatian Borna Coric has shocked world number one Andy Murray at the Madrid Masters.
World No.59 Coric, who won his first ATP title last month in Morocco, took the second break point to serve out for the match, sending last year's finalist and two-time Madrid victor Murray packing.
"I definitely think I need to be concerned about today", Murray added.
"My match against (Dominic) Thiem in Barcelona, I was disappointed to lose, but I felt like I competed really well".
However, Murray cut a frustrated figure as he was swept aside by the 20yearold Croatian for the second time in the pair's four meetings. "I wasn't winning too many points on his service games until the last one where I managed to return many balls back in play and then win the match".
"Whereas today I didn't really do any of that stuff".
Murray said: "Most things weren't working particularly well".
Dimitrov looked in fine fettle as he took moved a set and a break up against Theim, but the 23-year-old Austrian showed tremendous resilience to advance to a quarter-final against Coric.
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"Things can turn around quickly in tennis".
Coric, who lost in the second round of qualifying to Mikhail Kukushkin, got into the main draw when Richard Gasquet withdrew.
"Things change fast but you need to find exactly what it is that is going wrong and how you're going to fix that and commit to it".
"Novak is someone that I don t have good record (against)", said the Japanese.
"It wasn't until really nearly the last game where I said, OK, I'm going to try, and I stood way back behind the baseline", Murray said. "I have noticed it from the beginning".
The 20-year-old is one of the most unsafe young players on the tour, with the Croat holding a 2-1 head-to-head lead over Rafael Nadal, and beat Murray in one of their three meetings in the Dubai quarter-finals back in 2015.
And he rammed home his advantage by breaking the fragile Murray serve again to close out the set.
But after failing to capitalise the Scot looked distracted as he remonstrated with his coaching staff as the second set went with serve until a bad eighth game from Murray gifted Coric the break once more.
Murray had two break points of his own in the next game but he could not take them and he was becoming increasingly irked at how the match was panning out as it reached a crucial stage at 4-3 to Coric.