The 26-year-old Bulgarian, who has claimed three titles this season, comes into the season finale as the world No 6 on the back of his most consistent campaign of his career.
Dimitrov, playing his first match at the ATP Finals, fell behind 0-15 at 6-5 but converted on his third match point for the win.
Instead of sending the match in the tie break, Dominic played an terrible service game to get broken again and fell 6-5 behind, hitting costly double faults to reduce his chances, and Dimitrov sealed the deal with a solid hold in game 12.
His breakthrough win coupled with Rafael Nadal's withdrawal from the tournament with a knee injury leaves Dimitrov poised to reach the semi-finals.
Having dominated a first set in which his opponent managed to get just 33 per cent of his first serves into play, Dimitrov should have won in straight sets.
In the absence of Novak Djokovic and Andy Murray, all eyes are on a potential showdown in London between Nadal and Roger Federer, who started his bid for a seventh ATP Finals title with a straight-sets victory against American Jack Sock on Sunday.
It was Thiem, who made his debut at the event previous year, who started nervously, allowing Dimitrov to ease to the opening set.
Dimitrov broke in the seventh game of the decider to take control once more.
A shanked forehand wide gave Thiem a set-clinching break at 6-5 but Dimitrov again pulled ahead in the third, when a sensational drop-volley put him a break and 4-3 up.
Thiem, ranked fourth in the world, won the Rio Open and was a finalist in Barcelona and Madrid.
"I think the best is yet to come".
"I'm not going to lie - I was pretty nervous, my first match out here", he told reporters. I was like, Not again, definitely not again.