Defending champion Djokovic was made to sweat before beating Germany's Jan-Lennard Struff in four sets on the first day.
Djokovic credited the pre-eminence of the Big Three over so many years to each player motivating the others, turning their rivalries into the stuff of legend.
Nadal, currently No. 1 in the ATP rankings, and Djokovic, who is No. 2 ahead of Federer, each took home two major trophies last season.
Players who took part included Rafael Nadal, Roger Federer, Serena Williams, Caroline Wozniacki and Alexander Zverev.
Check out the five players to watch in the men's draw at the Australian Open, the first Grand Slam tournament of the season.
Novak Djokovic is gunning for his eighth crown and Federer his seventh, having last lifted the Australian Open in 2018.
Their wins ensured Spain and Serbia clinched their ties at the inaugural 24-nation team event, where the countries are split into six groups across Sydney, Brisbane and Perth.
Tsitsipas gets his tournament underway against rising Canadian star Dennis Shapovalov on Friday morning.
Spain will make its second straight semifinal appearance after Nadal and Marcel Granollers defeated Máximo González and Leonardo Mayer 6-4, 4-6, 6-3 in the decisive doubles match.
The Serbian upped his game at the start of the second set but Federer saved the one break point he faced and broke twice to canter to victory.
Thiem broke his opponent at the first opportunity in the second set and, with Djokovic's error count climbing, went on to level the match.
Six-time champion Federer was beaten 7-5, 7-5 in the evening match on the opening day after Djokovic had swatted aside debutant Matteo Berrettini in the earlier Group Bjorn Borg contest in London.
The Spaniard, who has never won the ATP Finals despite his trophy-laden career, dethroned Djokovic from the top of the rankings this week.
Their group clash in London will only be the best of three sets -- Austria's two-time French Open finalist Dominic Thiem and Italian Matteo Berrettini make up the quartet.
Djokovic slips down the rankings because he loses the points that he won a year ago in London when Nadal was absent.