The Lotto-Soudal veteran sprinter got the better of Australian Caleb Ewan (Mitchelton-Scott) and three-time road world champion Peter Sagan (BORA-hansgrohe).
"It's a nice one," Greipel said. "It was a pretty fast sprint but I could wait as long as I wanted, It's nice to be back here this way after a few years of absence.
Greipel will wear the overall leader's into tomorrow's stage with a four-second time buffer over Australian duo Ewan and Will Clarke (Education First-Drapac).
Three riders got the race started, Clarke, Nicolas Dlamini (Dimension Data) and UniSA-Australia's Scott Bowden, and set about establishing more than a five minute lead on the peloton.
Bowden eventually dropped off while Clarke and Dlamini went on with the breakaway and battling for the major sprint and mountains points on offer.
As they parried the peloton turned up the pace and with 50km of road left the time gap was down to two minutes.
Dlamini then let Clarke take the front alone after having claimed all the mountain points on offer and securing the classification for the stage but he was eventually picked up by a peloton determined to set the stage for a sprint finish.
Greipel was asked if the stage win was dedicated to the memory of his mother Gudrun who died in early December after a four-year battle with motor neuron disease.
"My whole career is dedicated to her," he said. "She was my biggest supporter, all my career and I know she keeps looking."
Greipel will not live down the post-Tour de France comment about losing his racing instincts but is rapt with how the year has started.
"It was a big disappointment, then you say stupid things," he said. "It's nice when you're 35 and everyone tells you, you will get slower. But I don't feel it and I really like to race my bike."
Norwegian rider Daniel Hoelgaard (FDJ) crashed heavily on the last bend as the sprint trains set up for the finish and he was taken away by ambulance.
It is proving a bad Tour for Norwegians - Hoelgaard's compatriot Kristoffer Halvorsen (Sky) crashed in the People's Choice Classic on Sunday night and the Team Sky rider was ruled out of the race with a bone fracture in his right hand.
The Tour continues on Wednesday with a 148km stage in the Adelaide Hills and Greipel could lose the overall lead on the climb to the Stirling finish.