He served under 50% and he needed more than that to avoid those break points he had to play against, but he had a chance to fight until the very end, breaking Grigor's serve in the 10th game of the final set, when Bulgarian served for the win.
Serving for the match at 5-4, however, he wobbled again as a framed backhand beyond the baseline allowed Thiem a reprieve.
"I'm not going to lie, I was pretty nervous in my first match out here", Dimitrov said.
Dimitrov passed up his first chance to serve out the match in a tense third set but made no mistake two games later to triumph in the day's opening match in London.
Thiem grew in confidence as the match progressed into the second set and thanks to a higher percentage of first serves put the pressure on Dimitrov's shoulders, who was broken in the 12th game of the second set to force the decider.
In a topsy-turvy decider, Dimitrov engineered a break and served for the match only for Thiem to hit back, but that only brought a stay of execution for the Austrian, who served two double faults to hand the advantage back to his opponent.
Dimitrov, the Cincinnati Masters champion, suffered a last-16 exit in his previous tournament appearance at the Paris Masters but showed no signs of early nerves in a hard-hitting encounter.
Thiem gave his best to make a winning start at the ATP elite event but his efforts were not enough to earn the victory for him, coming to London in a poor form after reaching just 1 quarter-final since Roland Garros.
In the other match in the Boris Becker group, rising star Alexander Zverev beat Marin Cilic in three sets.