The Dutch driver took Van Amersfoort Racing's first F2 win at the Red Bull Ring, having lined up 11th before getting lucky with a tyre gamble.
Though Frederik Vesti led for much of the 40-lap race, a safety car with 12 laps remaining allowed Verschoor, who started on the soft tyres rather than the super softs, to make a well-timed stop.
Both he and Ayumu Iwasa (DAMS) took full advantage of their fresher tyres and carved through the field, finally passing Vesti on the penultimate lap for first and second, with the Prema driver in third.
It marked VAR's first F2 win, coming in just their second season in the series, while Verschoor was disqualified from last year's race at the same venue while driving for Trident for having too little fuel left.
He dedicated the win to Dilano van 't Hoff, the 18-year-old Formula Regional driver who died at Spa on Saturday and whom Verschoor counted as a good friend.
Victor Martins lined up on pole for Sunday's race in far drier conditions than Saturday's race, starting on the super soft tyres ahead of Vesti and Theo Pourchaire (ART).
It was Vesti who got the jump off the line, quickly building a lead to his title rival, with Kush Maini moving into third for Campos Racing before he was passed by Jack Doohan (Virtuosi).
Virtuosi driver Amaury Cordeel was first to pit for the harder compound tyre, with Pourchaire among those to follow suit the following tour on lap eight.
Doohan and Martins were next to stop, before Vesti pitted at the end of lap 10 and handed the lead to Rodin Carlin driver Enzo Fittipaldi, who was running on the alternate strategy, starting on softs.
Vesti climbed through those who were yet to pit as Pourchaire followed, but with his older tyres, the Sauber junior was passed by Doohan up the inside of Turn 3 on lap 25.
The safety car was deployed on lap 28 after Arthur Leclerc lost a wheel from his DAMS-run car which had not been fitted properly, the right rear tyre bouncing across the track and forcing him to stop.
Fittipaldi pitted under the safety car after a strong stint, but his stop proved to be poorly timed, and he emerged behind a pack of traffic into ninth.
Verschoor, meanwhile, had come out in sixth, making his way up to fourth once the safety car ended.
He passed Pourchaire on lap 33 with Iwasa following him through as they got temperature into their soft tyres, though the virtual safety car on lap 35 briefly paused their climb.
A four-way battle for the win emerged between Vesti, Doohan, Verschoor and Iwasa, but the two alternate strategy runners had far fresher tyres and easily passed Vesti and Doohan.
Doohan finished fourth for his best result since Saudi Arabia, with Ollie Bearman in fifth for Prema.
Fittipaldi settled for sixth after the strategy failed to pay off, with Pourchaire seventh after struggling with older tyres.
Saturday's sprint winner Jak Crawford, Martins and Jehan Daruvala (MP Motorsport) rounded off the top 10.
| Cla | Driver | Team | Gap |
|---|---|---|---|
| 1 |  Richard Verschoor |
Van Amersfoort Racing |
|
| 2 |  Ayumu Iwasa |
 DAMS |
|
| 3 |  Frederik Vesti |
 Prema Powerteam |
|
| 4 |  Jack Doohan |
Invicta Virtuosi Racing | |
| 5 |  Oliver Bearman |
Prema Powerteam |
|
| 6 |  Enzo Fittipaldi |
Rodin Carlin | |
| 7 | Theo Pourchaire |
ART Grand Prix |
|
| 8 |  Jak Crawford |
Hitech Pulse-Eight | |
| 9 | Victor Martins |
ART Grand Prix |
|
| 10 |  Jehan Daruvala |
MP Motorsport |
|
| 11 |  Dennis Hauger |
MP Motorsport |
|
| 12 | Isack Hadjar |
Hitech Pulse-Eight | |
| 13 | Clement Novalak |
Trident |
|
| 14 |  Ralph Boschung |
 Campos Racing |
|
| 15 |  Zane Maloney |
Rodin Carlin | |
| 16 |  Roy Nissany |
PHM Racing by Charouz | |
| 17 |  Amaury Cordeel |
Invicta Virtuosi Racing | |
| 18 | Juan Manuel Correa |
Van Amersfoort Racing |
|
| 19 | Brad Benavides |
PHM Racing by Charouz | |
| 20 | Kush Maini |
Campos Racing |
|
| 21 |  Arthur Leclerc |
DAMS |
|
| 22 |  Roman Staněk |
Trident |
|
| View full results | |||
