The race high attrition rate became obvious from the start. Nico Hulkenberg's engine let go early in the race while pole-sitter Valtteri Bottas had a gearbox failure.
The second incident prompted a virtual safety car and a mad dash to the pits for most of the leading contenders.
Leader Hamilton stayed out – unsure whether the chasing bunch would follow him in or not – but was the only major player to stay on track. Eventually he made a stop 10 laps later to limit the damage.
In what became a disaster for the Brit, his next set of tyres blistered and he required another pit stop and then just when he could see his championship lead evaporate a loss of power ended his race early.
Birthday boy Daniel Ricciardo also suffered a mechanical DNF.
Sauber had a double points finish through Marcus Ericsson and Charles Leclerc while the McLaren of Fernando Alonso finished eighth after starting from pit lane.
Dutchman Verstappen made a strong start and seemed to be able to get the best out of his tyres as others ran into problems.
He had the Ferrari of Raikkonen chasing him down in the closing stages but had enough in reserve to score a win at the home of Red Bull.
"It's amazing to win in a Red Bull at the Red Bull Ring," Verstappen said.
"To win around the Red Bull Ring with all the Dutch fans here is incredible. Today was definitely a very good day"
Raikkonen, under pressure to retain his seat at Ferrari next year, didn't have enough to challenge for the win.
"The car came very good but we just ran out of the laps - we took it easy too long," Raikkonen said.
Vettel got a horror start, dropping places on the opening lap when he got squeezed wide and was playing catch-up from the start of the race. His good fortune came largely through failures to his rivals.
"I tried to get some [places] back at the start but was left with nowhere to go and it was the same at Turn 3," Vettel said. "It was damaged limitation for us."
Vettel takes the lead of the championship by one point as the series moves to Silverstone for the British Grand Prix next week.