Dominic Thiem avenged his defeat by Stefanos Tsitsipas in the championship match at last year's ATP Finals in the opening encounter of the eight-man elite tournament in London on Sunday.
US Open champion Thiem stumbled after winning the first-set tie-break but found his range again to win 7-6 (7/5), 4-6, 6-3 and seize the early initiative in Group London 2020.
In the evening match in the group, second-seed Nadal, appearing at the end-of-season event for a 10th time, takes on Russian debutant Andrey Rublev.
The 20-time Grand Slam champion, who has never won the tournament, has qualified for the ATP Finals for a record 16 consecutive years but has missed six editions due to injury.
Thiem, 27, was impressive on serve in the first set but failed to convert three break points against the Greek world number six in an empty O2 Arena.
The Austrian third seed found himself in deep trouble when trailing 4-1 in the tie-break but battled back and made his first set point count when Tsitsipas went long with a backhand lob.
Tsitsipas responded well, capitalising on forehand errors, and fired a forehand passing shot down the line to claim the first break of the match in the third game, going on to level the match.
The defending champion appeared to have the momentum but Thiem rallied impressively, earning a break with a delicately dinked forehand at the net in the second game of the decider.
The fifth game ultimately proved to be decisive. Tsitsipas had a chance to break but caught the net with a powerful backhand and could not engineer another break point in a game that contained six deuces.
Thiem ended the match with a confident service hold as his 22-year-old opponent fired a forehand wide.
"I think the level was higher last year," said Thiem. We were both in great shape last year in the final, we wanted that title 100 percent. The atmosphere was insane last year in the final and today was a little bit different.
"It was a lot over the serve for both of us, only two breaks in the whole match. I think the conditions are pretty fast here so I'm super happy with my win.
"Every win against a top-10 player here at the finals is something special and as well every win against Stefanos is something special."
Earlier, Novak Djokovic received the ATP Tour No. 1 trophy after finishing the coronavirus- interrupted year at the top of the rankings for a record-equalling sixth time.
The Serbian, who has drawn level with American Pete Sampras, said: "Obviously I am super proud of it, but I have mixed emotions because of what is going on in the world. I can't be ignorant to that, although I have achieved one of the biggest goals in sport."
Top seed Djokovic, who is competing in Group Tokyo 1970 alongside Daniil Medvedev, Alexander Zverev and Diego Schwartzman, plays his opening match on Monday.
The O2 Arena is hosting the ATP Finals for the 12th and final season before the year-end championships moves to Turin next year.