
Argentine 10th seed David Nalbandian pulled up perfectly after straining a back muscle last week at Kooyong, swamping Australian Robert Smeets 6-1, 6-1, 7-6 (7-3) to work his way into the tournament.
Serbian third seed Djokovic, who lost the final of his last Grand Slam, the US Open, to Roger Federer, was almost tripped up in the third set by Becker, who ended Andre Agassi's career at the 2006 US Open.
Djokovic's level dropped slightly in the third set, which lasted longer than the first two combined, but the seed ended it with a cross-court winner off a let cord bounce. The defeat was the fifth in a Grand Slam first round for Becker.
"I was nervous before the match, knowing that I'm a big favourite in the first round against a player, who is in the top 100 for two years," said Djokovic.
"I was really focused on the start and just tried to think about the match and the court and what happens there. But I lost my momentum a little bit in the third set.
"It's good to win in the straight sets and not to experience the big heat, which is one of the trouble factors here in Australia."
Spanish fifth seed David Ferrer put an early loss last week in New Zealand out of his mind with a 6-2, 6-2, 6-1 crushing of Edouard Roger-Vasselin of France.
Australian hopes sagged on another day of perfect weather and the potential for a further attendance record.
South Korea's Lee Hyung-Taik put an end to the hopes of Sydney finalist Chris Guccione, destroying the big man 7-6 (8-6), 6-3, 6-4.
Guccione was one of 10 locals figuring in matches on the day.
Women's second seed Svetlana Kuznetsova was untroubled by France's Nathalie Dechy 6-3, 6-1 while Russian sixth seed Anna Chakvetadze didn't have to fire a shot as German first-round opponent Andrea Petkovic hurt a knee during warm-up and could not play.
Ninth seed Daniela Hantuchova of Slovakia advanced over American Vania King 6-3, 7-5 while India's Sania Mirza started her fortnight with a win over Iroda Tulyaganova 6-4, 6-2.