The Dutchman, who celebrated his 26th birthday last weekend, clocked a best lap in one minute and 27.428 seconds to outpace the Ferraris of Carlos Sainz and Charles Leclerc by 0.334 and 0.481 seconds respectively.
Two-time champion Fernando Alonso of Aston Martin was fourth ahead of Sergio Perez, the only remaining title rival to Verstappen, in the second Red Bull.
Verstappen holds a lead of 177 points in the championship ahead of Perez, a luxurious advantage that means he will take his third consecutive title on Saturday if he scores at least three points, by finishing eighth or better, in the sprint race.
On the early evidence, it appeared he and Red Bull might dominate qualifying later Friday and attempt a clean sweep of the weekend.
In hot and tricky conditions with a strong cross-wind, Yuki Tsunoda was sixth for Alpha Tauri ahead of Nico Hulkenberg of Haas, George Russell of Mercedes and the two McLarens of Oscar Piastri and Lando Norris.
Seven-time world champion Lewis Hamilton was 13th for Mercedes, more than 1.2 seconds adrift of Verstappen's pace.
The session began in sultry late-afternoon conditions at the Lusail International Circuit, a strong breeze bringing much sand and dust across the track as the drivers prepared to run on the resurfaced asphalt.
Mercedes team boss Toto Wolff was absent again, for a second race weekend, following a knee operation, but his team, according to Hamilton, knew he was 'fully engaged' with their track operations.
Verstappen was one of many to make a swift start to the action and immediately reported on the conditions.
"Oh, my god, it's so slippery," he said, a view supported by Sainz, as Alonso set the early pace for Aston Martin.
The track temperature was 46 degrees Celsius and the air temperature 34.
Russell then took control and was 1.5 seconds clear of Pierre Gasly in 1:31.613, before Hamilton, who won the only previous Qatar Grand Prix in 2021, struck back in 1:31.279 as the Mercedes men diced at the front of the field.
Leclerc then took over on top in 1:29.082 before Alonso regained the initiative and, as the sun and the temperatures fell, Leclerc switched from hard to medium tyres and Verstappen survived a snap at Turn Six.
With 12 minutes remaining, Leclerc briefly went top before Alonso regain his place while Verstappen appeared to content himself in third, knowing he needs only to score three points – by finishing sixth or better – in Saturday’s sprint to secure his third drivers’ title.
As if scripted, however, the Dutchman surged to the fastest lap with two minutes remaining, his lap in 1:27.428 giving him a three-tenths advantage on Sainz as the chequered flag waved.
