The Serbian second seed's 6-3, 7-6 (2), 6-1 win over world No.96 Lukas Lacko on Monday night was comfortable enough not to cost Djokovic too much physical or emotional energy.
But he was stretched enough at times to provide the sort of competitive tune-up he needed in what was his first official match this year and first since hiring former world No.1 Becker.
Djokovic admitted he was rusty in the first two sets.
But he said his game clicked in the third and he expected his union with Becker to help him in his attempt to become the first man in the Open Era to win five Australian Opens.
"We both hope to get the right benefits and the right results right away here in Australia," Djokovic said.
"We worked very hard during the last four weeks. We believe that hard work will pay off.
"He definitely has great observations on my game, on tennis in general.
"The understanding is great in the beginning. I did not expect ourselves to understand each other so well right away in the second or third week that we working are with each other."
Djokovic entered the tournament on a 24-match winning streak, which followed his loss to world No.1 Rafael Nadal in last year's US Open final.
He was also on a 21-match winning streak at Melbourne Park, having won the Open for the past three years, to go with his breakthrough 2008 triumph.
But, while he was always in control, he wasn't always at his best early in the match.
Djokovic gained an early break to take a 4-1 lead, but Lacko broke back comfortably in the seventh game of the first set.
It seemed to spur the Serb on, as he lifted his aggression in the next game to quickly notch another break, then served out the set.
Lacko made him work even harder for the second set, with no breaks of serve and barely an opportunity throughout.
But Djokovic again asserted his class to dominate the tiebreak.
By then, any sniff of an upset was gone and Djokovic raced through the last set in 23 minutes.
"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," he said.
"It came at the right time, in the tiebreak in the second, and the whole third set was great."
It was Lacko's fourth successive first-round loss in a grand slam event.