The Dutch Red Bull star took the chequered flag after a drama-filled showdown ahead of Mercedes' Hamilton for his second win of the year and first in Melbourne.
He started from pole but was passed by both George Russell and Hamilton as they jostled for position at the start.
His superior Red Bull power eventually brought him home, but he had a dig at Hamilton nevertheless, complaining that the British seven-time world champion pushed him wide.
"From my side, I just tried to avoid the contact, it's quite clear on the rules what is allowed to do now on the outside, but clearly, it's not followed," he said.
"But that's OK. We had good pace, we passed (Hamilton) anyway but it's something for the next race to take into account."
A revived Hamilton, who finished second for his best result of the year, denied he was in the wrong.
"I thought it was pretty decent. He braked early and I braked late. I was fully up to his side and I think we both left space for each other," he said.
"I didn't run him off the road, he didn't turn in on me. We didn't touch and that's racing."
Despite the early close call, Verstappen was able to regain the lead and once he did never looked threatened, despite the race being red flagged three times, including with two laps to go.
"Of course, I was very happy to get the win but I think the race towards the end was a bit of a mess with all the calls," he said of the red-flag issues. "It left a lot of drivers confused."
Verstappen's straight line speed was again clearly better than his rivals in Melbourne.
But improvements from Hamilton's Mercedes and the ever-present threat from third-place Fernando Alonso gave them reason to hope he can be caught.
The Dutchman said it was too early to tell if they were closing the gap.
"I think it was the nature of the track a bit, that all made it all a bit closer," he said.
"I think also the warm-up was quite tricky, some teams nailed it better than others, so difficult to say. I think we need to go to a few more tracks to have a full understanding."
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