Novak Djokovic and Carlos Alcaraz took their first step toward a potential quarterfinal showdown at the Australian Open, with both winning their opening matches Monday.

After dropping his opening set to Nishesh Basavareddy, an American who left Stanford University and turned pro last month, Djokovic eventually asserted himself for a 4-6, 6-3, 6-4, 6-2 victory to begin his bid for an 11th championship at Melbourne Park and a record 25th major title overall.

It was Djokovic’s first match with former rival Andy Murray as his coach. Murray retired as a player at the Paris Olympics in August; Djokovic proposed teaming up in November.

This first-round match was Djokovic’s record-extending 378th victory at a major; he hasn’t lost in the first round of one since bowing out at that stage of his first two Australian Opens in 2005 and 2006.

He’ll next face another relative youngster in 21-year-old Portuguese Jaime Faria in the second round, looking to take another step towards a 25th major title.

Earlier Monday, Alcaraz began his bid to complete a career Grand Slam with an imperfect but entertaining 6-1 7-5 6-1 win over Kazakh Alexander Shevchenko.

Four-times major champion Alcaraz is targeting his maiden trophy at Melbourne Park to become the youngest man to capture all four Grand Slam titles, and the 21-year-old went all guns blazing after a slightly nervy opening game.

“I always say that it’s hard work,” Alcaraz said.

“I try to bring the best of me every day. That’s the secret. Every day I try to be a better person and better player.”

The third seed, still fine-tuning a new service motion that he adopted in the off season, fended off a break point and then broke in the third game to take full control of the opening set which he wrapped up in double quick time.

He found his range with some devastating winners on both flanks and went up 3-1 in the second set, but world number 77 Shevchenko won the next four games as fans on Margaret Court Arena got behind the underdog.

Alcaraz switched back on and struck a fiery forehand winner to set up another break point and drew level in the 10th game as his opponent began to feel the intense pressure again and went on to surrender the set.

With the momentum having swung definitively, Alcaraz reeled off games in the third set and finished it off with a big ace on his fifth match point to book a second-round meeting with Japan’s Yoshihito Nishioka.

“He’s a really solid player,” Alcaraz said.

“I have to be focused on my shots … Hopefully I can enjoy the match, it’s going to be tough. I’ll try to produce some good tennis for people to enjoy.”

Information from The Associated Press and Reuters contributed to this report.