Australian Oscar Piastri finished second, 4.6 seconds behind, with McLaren teammate Lando Norris, Verstappen's closest championship rival, ending up third after starting on the front row.
Norris passed Verstappen going into turn three on the fifth of 23 laps but could not hold the advantage and lost out to both drivers at turn four.
"That was spicy, wasn't it," said Verstappen over the team radio after taking the chequered flag for his third sprint win out of three this season.
Austria has the shortest lap on the calendar, in terms of time, and Verstappen found it hard initially to pull sufficiently clear to deny his rivals a drag-reduction advantage.
"Once we cleared the DRS, I could do my own race and it was better," he said.
"You could see they had two cars pushing flat-out trying to make it difficult for me."
George Russell was fourth for Mercedes and Carlos Sainz fifth for Ferrari. Their respective teammates Lewis Hamilton and Charles Leclerc were sixth and seventh with Red Bull's Sergio Perez eighth.
The top eight finishers in the 100km sprint score points, with the winner taking eight.
Qualifying for Sunday's main grand prix follows later on Saturday.
The first start was aborted because photographers standing behind the barriers at turn one were judged to be posing a safety risk. There was a second formation lap and the number of race laps was reduced to 23.
Verstappen got away cleanly, with Sainz passing Russell to move up to fourth, but Norris was right behind and soon enjoying the advantage of drag reduction.
The Briton dived down the inside at turn three but Verstappen hit right back, with both running slightly wide at the exit to turn four as Piastri sensed his opportunity and seized it.
Russell later passed Sainz for fourth on lap eight.
"Probably some things I definitely should have done a bit better in my battle. I understand that and the pace of the car was very strong, especially at the end of the race," said Norris, who said before the start that he was not feeling great.
"I had a good battle trying to get past Oscar but just didn't have enough speed.
"Once the tyres get too hot it's difficult to do too much, so I had to make the most of my opportunity. Then I messed it up and left the door open like an amateur."
McLaren team boss Andrea Stella said there was no consideration of switching the drivers around, with Piastri sixth in the championship and far behind Norris on points.
"He deserved to be in P2 because he gained it on track and there was really no necessity, at least for the team, to force the natural order of the sprint race," the Italian told Sky Sports television.
"We are happy like this. Well done to both of our drivers."
