Alcaraz recovered from a chaotic opening set to triumph 7-6 (5), 6-2 over seventh-seeded De Minaur in the opening match of the season-ending event for the top eight men’s players.
Ben Shelton saw three set points saved on his ATP Finals debut, with two-time champion Alexander Zverev beating the American 6-3, 7-6 (6).
Top seed Alcaraz is locked in a battle with defending champion Jannik Sinner to end the year as No. 1 and the Spaniard can secure that – no matter what his rival does – if he reaches the final.
It was the first time that Alcaraz won his ATP Finals opener.
“This tournament is without a doubt one of the best tournaments we have on tour,” Alcaraz said. “We are playing against the best players in the world, which shows how difficult and important it is.
“I’ve struggled in recent years to get to the end of the year motivated. This year it’s a little different, which I’m proud of. I’m doing the right things to give myself a chance to win this tournament.”
Alcaraz seemed to have the opening set firmly under control. He had already broken De Minaur to love and threatened to do the same in the sixth game to take a 5-1 lead, but the Australian fought back to deuce before staving off another break point and then taking the match.
De Minaur then broke back to take the set to a tiebreak, where he took a 5-3 lead before Alcaraz rallied.
The 22-year-old Alcaraz dominated the second set, dropping his serve early, but won all other games and sealed the victory with a cross-court backhand on his second match point.
Taylor Fritz is also in Jimmy Connors’ group with Alcaraz, De Minaur and Lorenzo Musetti, who replaced the injured Novak Djokovic.
The Bjorn Borg group consists of Sinner, Zverev, Shelton and Felix Auger-Aliassime.
It took third-seeded Zverev just 28 minutes to wrap up the first set against Shelton, who then appeared to shift gears and get a big chance to level the match in the second-set tiebreak.
Shelton took a 4-0 lead and squandered three set points before sending a backhand wide to give Zverev victory after 93 minutes.
The top two finishers from each group will advance to the semi-finals.
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