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 (25) 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," Verstappen 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 (41) 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."
Hamilton ecstatic after Mercedes' troubles
Lewis Hamilton was "super grateful" to take his first podium of the year, and suggested Mercedes could close the gap on the dominant Red Bulls.
It was his best result of the year and hugely encouraging after a miserable season last year for his struggling team.
"I didn't expect to be second so I'm super grateful for it," he said.
"I'm driving as best I can and working as hard as I can but still, considering we've been down on performance and in straight pace, for us to be up there fighting with Aston is amazing.
"We can close that gap (to Red Bull)," he added. "It's going to be tough but not impossible."
In contrast to Hamilton's podium, teammate Russell failed to finish after his car caught fire after starting second on the grid.
Hamilton said it was "really unfortunate" for Russell, but couldn't hide the fact that Mercedes were making progress.
"It was very unexpected (getting second) coming into the weekend, but obviously getting two and three in qualifying yesterday blew us all away," he said.
"It was huge boost of energy throughout the team and then today we had a shot at trying to at least overtake Max for a second and we both got ahead, which was amazing to have a Mercedes 1-2 before he came sailing by."
His stirring battle with Alonso - a former teammate - was enthralling, with Hamilton saying his car had better speed on the straight but the Aston Martin excelled on the corners.
"So I think we definitely have some performance to find, it definitely wasn't easy keeping him at bay," he said of the Spaniard.
"But it was really quite interesting to see where we were lacking and where we were good, so there's lots of positives to take from today.
"For us to still somehow finish ahead (of Alonso) is pretty awesome and I'll take it."
