Following his triumph at the French Grand Prix week ago, Verstappen holds a 12-point advantage over Hamilton.
And on the evidence of the first running at the Red Bull Ring, the Dutchman remains the man to beat.
Verstappen ended the one-hour running two tenths clear of Gasly, while Hamilton was 0.422 seconds adrift of his title rival.
Valtteri Bottas in the other Mercedes finished fourth, half-a-second back.
The Silver Arrows have dominated Formula One, winning the past seven drivers’ and constructors’ championships.
But they are facing a stern examination of their credentials with Verstappen’s triumph at Circuit Paul Ricard last Sunday, Red Bull’s third in succession.
For the start of two consecutive weekends in Austria, a number of drivers were caught out by the green conditions, with Carlos Sainz spinning his Ferrari on the main straight – and temporarily blocking the pit lane – while Verstappen’s Red Bull team-mate Sergio Perez also spun at Turn 4 but headed back to the pits without any damage.
The Mexican finished only 13th in the standings, eight tenths off Verstappen’s pace.
Elsewhere, rookie Yuki Tsunoda was fifth on an encouraging morning for AlphTauri, one spot ahead of Alpine’s Fernando Alonso.
Lando Norris is fifth in the championship after a strong start to his third campaign on the grid. But the British driver finished only 16th for McLaren in the first running. Williams driver George Russell was one place ahead of his compatriot.
The drivers are due to be back on track at 2pm but rain is on the radar and could impact the second scheduled action of the weekend.