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.
Again Dimitrov wobbled, squandering two match points at 40-15 with a double-fault and a tight forehand error, but he finally bagged the win when Thiem looped a backhand long.
"I'm not going to lie - I was pretty nervous for my first match here", Dimitrov said in his post-match on-court interview.
One break of serve was enough to take the opening set, but Thiem kept his composure to record the solitary break during the second to take the contest into a decider.
He slowly began to carve out opportunities on Dimitrov's serve, forcing his first break point as the set reached its conclusion, with the subsequent break helping him to force a decider.
Sudanese president to visit Uganda to fix bilateral ties
The two parties agreed to implement the decisions during the latest joint commission meetings held in Khartoum earlier this year. They are seeking opportunities for trade, investment and business partnerships with their Ugandan counterpart.
In the other match in the Boris Becker group, rising star Alexander Zverev beat Marin Cilic in three sets.
Dimitrov opened his charge in London with a determined 6-3 5-7 7-5 win over his Austrian counterpart, who is ranked two places higher in the rankings.
Later, Nadal takes on David Goffin in the second match in the Pete Sampras group, with questions over his fitness after the Spaniard admitted he was not training at 100 percent following his withdrawal from the Paris Masters with a knee injury.