Djokovic's 122-week reign as world number one was ended by Andy Murray last weekend.
Djokovic's 122-week reign at the top was ended by Andy Murray last weekend.
However, he can climb back into pole position by the end of the tournament if he lifts the Tour Finals title for a fifth successive year while winning at least two of his group stage matches.
The 29-year-old remains on track to achieve that target despite a shaky first set in the opening match of the prestigious season-ending tournament at London's O2 Arena.
And amid all the questions about Djokovic's decline, he can still clinch the season-ending number one spot for a third consecutive year and equal Roger Federer's record of six Tour Finals titles by the end of next week.
"Dominic started very well and we played on a very high level from the first point," Djokovic said.
"He had a very high serve percentage and was the tougher player in the key moments of the tie-break.
"I definitely did not want to let him get off to a good start in the second set."
Wimbledon finalist Milos Raonic beat flamboyant Frenchman Gael Monfils 6-3, 6-4 in the other match in Djokovic's group on Sunday.
Djokovic established himself in the pantheon of all-time greats in June when his French Open triumph made him only the fifth man in the Open era to complete a clean sweep of the four Grand Slam tournaments.
But since that historic triumph the Serb had been stuck in a puzzling slump that has seen him suffer embarrassingly early exits from Wimbledon and the Rio Olympics.
Having shaken off his early lethargy, Djokovic eventually blew Thiem away in emphatic fashion and is now 19-1 in his last 20 matches at the Tour Finals.
The world number two was in the wars early on when he needed a bandage on the thumb on his right hand after his racquet jammed into the court.
Another high-profile figure who has lost his magic touch of late, Manchester United manager Jose Mourinho, was watching from courtside and must have sympathised.
The 12-time Grand Slam winner staved off a break point at 5-5, but Djokovic remained an unsettled figure, grumbling to a line judge; "Was it in or out? Or do you just not know?"
Djokovic's gloomy mood was hardly improved when Thiem took the first set in a dramatic tie-break after the Serb had saved six set points and squandered one of his own.
He slammed a ball hard into the court once the set was lost and it bounced into the stands, drawing a warning for unsportsmanlike conduct.
In danger of another frustrating loss, Djokovic was finally able to turn his anger into a positive at the start of the second set as unloaded a series of powerful winners.
Two breaks in the first three games gave him a lifeline and he took the set without dropping a single game.
Thiem had won 21 out of his 23 matches that required a final set this year, but none of those came against Djokovic and the Serb kept his foot on the gas to win the third set in emphatic fashion.
London has been good to Raonic this year, with the Canadian reaching the finals of Wimbledon and Queen's, and he looked at home on his return to the English capital.
The 25-year-old broke in the second game of a first set which he won with minimum fuss.
Monfils, appearing in the Tour Finals for the first time, was no match for the big-serving Raonic and the world number four wrapped up the win after he broke in the seventh game of the second set.