Williams, looking for her sixth title, closed the evening on Rod Laver Arena with a 6-2 6-1 demolition of local hope Ashleigh Barty after four-times champion Djokovic had overcome Lukas Lacko 6-3 7-6(2) 6-1.
Earlier, there were shocks aplenty in the women's draw with the biggest coming when sixth seed Petra Kvitova fell victim to Thai world number 88 Luksika Kumkhum in front of a rapturous crowd on Margaret Court Arena.
There were upsets for two Italian seeds as well, Sara Errani beaten 6-3 6-2 by German Julia Goerges and her doubles partner Roberta Vinci going down 6-4 6-3 to China's Zheng Jie.
Serena's sister Venus Williams also bid an early farewell to the tournament when she blew a 3-0 lead in the deciding set to lose 2-6 6-4 6-4 to Russian Ekaterina Makarova.
Djokovic's new co-coach Boris Becker will have raised an eyebrow with the 30 unforced errors the second seed served up as he opened his quest for a fourth straight title in Melbourne.
The Serbian always looked like cantering to victory in three sets, however, and 23 minutes after taking a tight second stanza by dominating the tiebreak, he was firing down his 10th ace for the win.
"I know that I didn't play my best, especially in the second set," said Djokovic, who has now won his last 22 matches at Melbourne Park and 25 contests in a row in all tournaments since his loss to Rafa Nadal in the U.S. Open final.
"I was a little bit too passive in some stages of the match and was trying to find the proper setting and proper balance and footing in the court."
With temperatures forecast to soar well above 40 degrees Celsius from Tuesday onwards, there was good reason for the players to keep their time on court to a minimum and rest up for challenges to come.
Even in the cool of the evening, Serena Williams showed no signs of wanting to hang around and 17-year-old Barty looked like a lamb heading for the slaughter.
Williams, who hit 31 winners, feasted on the teenager's second serve and even dominated at the net, suggested that she herself was the biggest obstacle to her title ambitions.
"I just don't want to get in my way. I just have to stay out of my way and I'll be fine," she said.
"As long as I'm able to stay relaxed, I'll be okay."
Thai Luksika was far from relaxed as she looked to close out her victory over Kvitova but was soon bowing to all corners of the stadium having sealed the biggest win of her career 6-2 1-6 6-4.
"I was really excited to be here, feeling good," said former Wimbledon champion Kvitova. "I think that probably I wanted (it) too much, and then everything just fell down."
Fourth seeded Chinese Li Na never came anyhwere near being upset as she dispatched teenager Ana Konjuh 6-2 6-0 to set up a meeting with another 16-year-old, Swiss Belinda Bencic.
Bencic beat 43-year-old Kimiko Date-Krumm 6-4 4-6 6-3 in a battle of generations - the 27-year age gap between the two the widest at a grand slam since a 47-year-old Martina Navratilova was beaten by 19-year-old Gisela Dulko at Wimbledon in 2004.
Local hopes in the women's draw rest largely with Sam Stosur and the 2011 U.S. Open champion made a reasonable start on Monday, gaining revenge for a semi-final defeat in Sydney last week with a 6-3 6-4 win over Czech Klara Zakopalova.
Men's top 10 seeds David Ferrer, Tomas Berdych, Stan Wawrinka and Richard Gasquet earlier raced into the second round with three set victories, eager to make the most of relatively mild conditions at Melbourne Park.
Ferrer sprinted to a 5-0 lead in the first set before being drawn into a scrap with Colombian Alejandro Gonzalez but still ground out a 6-3 6-4 6-4 victory.
"The most important thing is to win. Today maybe I didn't play my best tennis, but I won," said Ferrer, the least favoured third seed at Melbourne Park for several years.
Swiss Wawrinka, Djokovic's potential quarter-final opponent, had the easiest passage when Kazakh Andrey Golubev retired while trailing 6-4 4-1.
German Tommy Haas, seeded 12th, also retired with a shoulder injury while losing to Spain's Guillermo Garcia-Lopez in his first round match.
Berdych and Gasquet both went through in less than two hours, however, the seventh seeded Czech beating Aleksandr Nedovyesov 6-3 6-4 6-3 and ninth seed Gasquet downing fellow Frenchman David Guez 7-5 6-4 6-1.
Spanish top seed Nadal gets his campaign underway on Tuesday along with two of the other "big four" of men's tennis, Wimbledon champion Andy Murray and 17-times grand slam champion Roger Federer.