MELBOURNE, Australia — Serena Williams claims to suffer from nerves and jitters before her first-round matches at the Grand Slams.

She certainly didn’t show it, winning her first set in 21 minutes on Tuesday night on the way to a 6-0, 6-4 win over Alison Van Uytvanck at the Australian Open.

The 18-time major winner has only once lost in the opening round at a Grand Slam tournament, and this is her 58th. One more Grand Slam title and she’ll pass Chris Evert and Martina Navratilova on the all-time list of champions.

“If I could get to 19 in Australia that would be amazing,” said the top-ranked Williams, who won the last of her five Australian titles in 2010.

Four-time Australian Open champion Novak Djokovic returned to Rod Laver Arena for the first time as a husband and father, shrugging off the effects of a cold to beat No. 116-ranked Aljaz Bedene 6-3, 6-2, 6-4 in his first-round match.

Djokovic won the first of his seven major titles at the 2008 Australian Open, then won here in three consecutive years from 2011 to 2013. His 25-match winning streak at Melbourne Park ended in a quarterfinal loss last year to Stan Wawrinka, who went on to win the title.

Wawrinka began the defense of a major crown for the first time with a 6-1, 6-4, 6-2 win over No. 100-ranked Marsel Ilhan, taking less than 1½ hours to breeze through the first round.

“It’s great, bringing me a lot of memories from last year,” Wawrinka said of his return. “It was great to come back here feeling happy, happy with my game.”

Top-ranked Djokovic had the subsequent match on center court and appeared to be tired and still recovering from illness after his match, saying he’d had a “rough two weeks health-wise but I’m getting up there.”

His mood changed suddenly when a court-side interview turned to reflections of 2014, when he won Wimbledon for the second time, married his long-time partner, Jelena, and the couple had a son, Stefan.

“Well those two events are the two most beautiful events I experienced in my life,” he said. “Stefan, he’s a blessing we received ... now I have even more motivation.”

Two other men widely considered to be in the next generation of major winners advanced in straight sets, with No. 5 Kei Nishikori beating Nicolas Almagro 6-4, 7-6 (1), 6-2 and No. 8 Milos Raonic firing 30 aces in a 7-6 (3), 7-6 (3), 6-3 win against qualifier Illya Marchenko.

The 33-year-old Lleyton Hewitt started his 19th consecutive Australian Open by beating Zhang Ze 6-3, 1-6, 6-0, 6-4.