Mercedes' seven-time world champion Hamilton finished a distant fourth, with teammate Valtteri Bottas second and McLaren's Lando Norris third, as Red Bull chalked up their fifth win in a row.
Verstappen led from start to finish at Austria's Red Bull Ring, with seven-time world champion Hamilton second for Mercedes.
The 23-year-old, now level with Hamilton on three wins for the season, also set the fastest lap and has 131 points to Hamilton's 119.
A tyre blowout denied Max Verstappen victory and Lewis Hamilton failed to score.
The 23-year-old Dutch driver started the day 14 points behind Mercedes' seven-time world champion Hamilton and ended it four clear.
The Briton's 98th career victory, from his 100th pole position, was his third win in four races and sent him 14 points clear of Red Bull's Max Verstappen.
Verstappen finished second at the Algarve circuit with Mercedes' Valtteri Bottas completing the podium, and taking a bonus point for the fastest lap, after starting from pole position.
Lewis Hamilton finished second for Mercedes and retained the lead in the championship by a single point.
Verstappen, who passed the Briton with four laps to go only to have to hand back the lead for exceeding track limits, finished a mere 0.745 seconds behind after starting on pole position.
The Mexican said he was adjusting to his surroundings after seven years with the Force India/Racing Point team that is now Aston Martin.