Soaking up the Rod Laver Arena limelight, the Serb moved superbly in his opener and hit 42 winners to wrap up the one-sided clash in little more than two hours.
Djokovic bowed out of the fourth round of last year's tournament bothered by a painful elbow injury but successfully came back from surgery to win Wimbledon and the U.S. Open.
Now free from fitness problems, the 31-year-old Serb is savouring his return to a tournament he has virtually owned for the last decade.
"It feels great to be healthy and back on this court again," the 14-times Grand Slam champion told reporters.
"Twelve months ago it was quite a different sensation on the court with the elbow injury. Twelve months forward, obviously things are quite different.
"Hopefully I can follow up on this victory tonight with a good performance."
Despite the scoreline, the 230th-ranked Krueger hardly disgraced himself and broke Djokovic in the third game of the first set.
That was as good as it got for the American, as the Serb knuckled down to break right back and coasted to an easy victory.
Djokovic watched injured 'Big Four' rival Andy Murray bow out of the first round in a gallant five-set defeat by Spanish 22nd seed Roberto Bautista Agut on Monday, and paid tribute to the three-times Grand Slam champion.
"After two sets, I think no one expected him to really come back, considering how he feels," Djokovic said of Murray's painful right hip.
"He showed once again his amazing champion spirit, why he's such a fighter, why he's so respected and appreciated around the tennis world, and sports world in general."
Djokovic will next meet French wildcard Jo-Wilfried Tsonga, the man he beat for the 2008 trophy and his first ever Grand Slam title at the age of 20.
"It's funny, I mean, 11 years after our first Grand Slam final here, it feels like a lot has happened for both of us," added Djokovic.
"He also struggled with injuries lately. It's good to see him playing well. It's good to see him back."
(Editing by Christian Radnedge)
