The Hitech driver started on slick tyres despite a damp track, slipping back off the line as those on wet tyres profited.
But as the Red Bull Ring dried and those ahead pitted for primes, he was able to claw back positions, and retook control on lap five.
From there, the Red Bull junior was able to build a 2.5s-lead to take his maiden win ahead of 2022 F3 champion Victor Martins (ART) and Trident driver Clement Novalak, who lined up 20th before charging through the field for his first podium since Zandvoort last year.
Despite wet conditions, the field lined up for a standing start on a mix of wet and slick tyres, with Crawford and Jehan Daruvala (MP Motorsport) opting for slicks with third-place starter Arthur Leclerc on the wets for DAMS.
Leclerc benefited from the additional grip to take second by Turn 1, while Crawford’s slicks proved ineffective and he fell to sixth, with Daruvala suffering a similar fate.
Championship leader Frederik Vesti started ninth on the wet tyres and was up to third by midway through the first lap, though his good fortune would soon run out as he was forced to pit for slicks.
Jack Doohan took a trip into the gravel at Turn 4 in his Virtuosi-run car before the safety car was deployed as Daruvala did the same at Turn 7, becoming beached.
Theo Pourchaire, who was running second, Vesti, Dennis Hauger (MP), PHM driver Brad Benavides and Ollie Bearman all pitted for slicks under the safety car, with Pourchaire handed a five-second penalty for an unsafe release between the two Prema cars.
The safety car ended on lap five but was almost immediately redeployed as Richard Verschoor, who had inherited the lead, spun out at Turn 1 and into the wall.
This left Leclerc to lead before the Monegasque driver and team-mate Ayumu Iwasa both pitted, handing the front spot back to Crawford, who led from Juan Manuel Correa (VAR) and Rodin Carlin driver Zane Maloney.
2022 F3 runner-up Maloney was then swamped on his wet tyres, with Martins taking his position as he fell back through the field.
Novalak, who had made an incredible charge through the field, took advantage of pitstops and incidents ahead, passed Isack Hadjar (Hitech) for fourth on lap 13 at Turn 4, as further back Bearman made it past Kush Maini (Campos).
Martins took second from Correa the following tour, using DRS to pass up the inside of Turn 3, though Crawford was still two seconds clear at the front.
Correa and Novalak then tussled for third over the closing stages, with both Novalak and Hadjar making it past the VAR driver, who fell to fifth.
Enzo Fittipaldi then spun his Rodin Carlin entry on the straight down to Turn 4 while running in 10th, having been forced onto the grass in his battle with Maini, prompting a virtual safety car.
Hadjar took fourth in his best result of the season so far, with Correa in fifth and Trident’s Roman Stanek in sixth, having also made a superb charge from 17th.
Hauger made it past Bearman and then Doohan in the final few laps to finish seventh, with the Australian rounding off the points-paying positions.
F2 Austria – Sprint race results:
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