The Red Bull driver started on pole and led from the off to take victory by 35 seconds at his team’s home race in Austria.
Hamilton kept Verstappen honest but never threatened to challenge as the Red Bull driver secured his second win in a week and fourth of the year, increasing his title advantage from 12 points to 18 with Hamilton securing a bonus point for the fastest lap.
Mercedes’ Valtteri Bottas took third, ahead of Red Bull’s Sergio Perez, with Lando Norris fifth for McLaren.
In a season of thrills and spills, Sunday’s showing in the Styrian mountains was more of a bore-draw than a seven-goal ding-dong.
After qualifying behind his rival, Hamilton feared only rain would save him, and despite his Mercedes boss Toto Wolff claiming there was a 60 per cent chance of showers during Sunday’s race, the poor weather stayed away.
At the start, pole-sitter Verstappen moved to his right to block Hamilton from making a move and was two seconds clear of the Mercedes following a handful of laps.
Behind, Norris managed to resist Perez’s advances on the opening lap, but could do little to stop the Mexican in his superior Red Bull from moving past on lap 10. Bottas followed suit the next time around.
Perez was the first of the leading quartet to pit, stopping on lap 26 of 71. But a sticky rear-left meant he was stationary for 4.2 sec, allowing Bottas to take third when he came in for tyres the next lap.
Hamilton and Verstappen stopped a lap apart, with the latter emerging from the pits five seconds down the road.
By the end of lap 58, Hamilton was the best part of 10 seconds adrift.
“What shall I do?” he asked his race engineer, Peter Bonnington. “I can’t close the gap.”
Bonnington could offer no real answer, other than calling on his driver to look after his rubber in the hope Verstappen’s would not last. However, the victor lapped the entire field up to fourth.
In a late roll of the dice, Perez stopped for a second time to hunt down Bottas in the battle for the final spot on the podium. The Mexican crossed the line just half-a-second behind the Mercedes driver.
AlphaTauri’s Pierre Gasly retired at the end of the first lap following a rear suspension failure after contact with Ferrari’s Charles Leclerc, while George Russell was the only other man not to finish.
Russell, 23, was running as high as seventh before an engine failure cruelly denied the Briton any hope of scoring his first points for Williams.
Additional reporting by PA.