Verstappen, who had lost the lead earlier in the race to George Russell and Lewis Hamilton, was back in front and looked to be cruising to victory until the late drama.
Max Verstappen secured his first-ever Australian Grand Prix victory in a nail-biting race that culminated in a safety car lap following a late restart.
The race had already been disrupted by two red flags when Kevin Magnussen crashed his car, setting up a two-lap sprint to the finish.
Hamilton was hot on Verstappen's heels during the restart, but a crash involving Fernando Alonso and Carlos Sainz set off a chain reaction of collisions, with Alpine team-mates Pierre Gasly and Esteban Ocon taking each other out of the points-scoring positions.
A third red flag caused further confusion and controversy, as the FIA took a long time to decide to restore the order from before the restart to complete the one remaining lap behind the safety car.
Alonso finished in third place, while Sainz was penalized for the collision and relegated to twelfth.
Aston Martin's Lance Stroll finished fourth behind team-mate Alonso, while Sergio Perez produced a solid recovery drive to finish fifth after starting from the pit lane.
Russell, who gave up the lead while pitting under safety car conditions and was not expecting the red flag that followed, retired due to a technical failure on lap 18.
Ferrari's Charles Leclerc retired on the first lap, leaving the team pointless.
Before the controversial climax, Verstappen had dispensed with an early challenge from Mercedes' Russell and to dominate the race.
The grand prix featured two safety car periods and a first red flag caused by a crash between Ferrari's Charles Leclerc and Stroll at Turn Three on lap one, followed by a heavy crash by Alex Albon's Williams at Turn Six.
Verstappen made a bad start and dropped behind the Mercedes cars but ran third for a while. He then took the lead from Hamilton two laps after the restart, and had opened up a 10s gap.
Verstappen was in total control of the race once he took the lead, demonstrating the advantage that the Red Bull car has over the rest of the field.
Despite making two poor starts during the weekend, he was able to showcase the speed of the Red Bull car and overtake Hamilton with ease using the DRS overtaking aid on the straight up to the fast Turn Nine/10 chicane.
Lando Norris drove an impressive race to finish sixth and secure McLaren's first points of the season, with rookie team-mate Oscar Piastri taking advantage of the late chaos to claim his first points in the sport and finish eighth at his home race.
Nico Hulkenberg finished seventh for Haas, while Alfa Romeo's Zhou Guanyu and AlphaTauri's Yuki Tsunoda rounded out the points after receiving late promotions.