Verstappen took pole position with a last-gasp 1m15.915s effort, bettering a still-recovering Carlos Sainz by 0.170 seconds.
Sergio Perez will start from third with Lando Norris the highest-placed McLaren driver in fourth.
Charles Leclerc had been the pacesetter in the early stages of the weekend but an error on his final lap scuppered his chances to start from the front, leaving him fifth. He will be joined on the third row by Oscar Piastri.
While George Russell qualified seventh, his Mercedes team-mate Lewis Hamilton struggled for pace and bowed out in Q2, setting the 11th-fastest time after a late improvement from Yuki Tsunoda - who will start in eighth - bumped him out of the top 10.
The third round of the 2024 F1 season, the Australian GP, gets under way at 3pm local time on Sunday 24 March.
In the United Kingdom, Formula 1 is broadcast live on Sky Sports, with highlights shown on Channel 4 several hours after the race has finished. Live streaming through NOW is also available in the UK.
Sky Sports F1, which broadcasts the F1 races, can be added as part of the Sky Sports channels and costs £18 a month for new customers. Sky Sports can also be accessed through NOW with a one-off day payment of £11.99 or a monthly membership of £34.99 per month.
In the United Kingdom, Sky Sports will be live broadcasting the Australian GP.
Source: Autosport