Valtteri Bottas completed the podium with Sebastian Vettel in fourth and Lewis Hamilton in fifth.
But the big talking point came on lap 69 when Verstappen and Leclerc bumped wheels as the Red Bull man took the lead in controversial circumstances.
It came after a wretched start for Vertsappen which saw Hamilton and Bottas move up ahead of him, and the Dutchman drifted deep down the pack until he resolved a problem with his battery.
Max Verstappen of Netherlands and Red Bull Racing during the F1 Grand Prix of Austria at Red Bull Ring on June 30, 2019 in Spielberg, Austria.
Image credit: Getty Images
Meanwhile, leader Leclerc was able to establish a lead over the Mercedes and pressed his team to be allowed to push the pace, with team-mate Vettlel, in fourth, cutting into the gap ahead of him.
Midway through the race Hamilton was given the chance to push with his first set of tyres while briefly holding top spot before his own pitstop, he reported problems with his front wing, and the replacement forced him down into fifth behind Vettel.
On lap 50, Verstappen’s raw pace saw him glide past Vettel into third, and when Vettel pitted onto soft tyres in response, Hamilton was able to move up into fourth. Six laps later, Verstappen swept into second and set up a chase with Leclerc before the thrilling finale.
Ferrari's Monegasque driver Charles Leclerc, Toyoharu Tanabe, F1 Technical Director of Honda, Red Bull Racing's Dutch driver Max Verstappen and Mercedes' Finnish driver Valtteri Bottas stand on the podium after the Austrian Formula One Grand Prix in Spie
Image credit: Getty Images
With only a few laps remaining, Leclerc and Verstappen battled wheel to wheel, with a nudge from the Red Bull driver edged the Monegasque off the track and claimed a brilliant victory. Championship leader Hamilton could only finish in fifth.
DRIVER OF THE DAY - Max Verstappen
He was hamstrung by some mixture of a poor start and technical problems, and he seemed to have wasted a chance to properly challenge for a rare race victory after a difficult campaign so far. However, his aggression and pace once the problems were resolved were key to his victory.
Red Bull Racing's Dutch driver Max Verstappen celebrates on the podium after the Austrian Formula One Grand Prix in Spielberg on June 30, 2019. - Max Verstappen won the Austrian Grand Prix after overtaking Charles Leclerc's Ferrari in the closing laps wit
Image credit: Getty Images
TALKING POINT - Was the takeover from Verstappen fair?
It certainly appeared to be a risky move. He definitely had the pace to chase down his rival, and it did not appear particularly dangerous. However, with Verstappen’s history, there must have been some doubt over whether he would be allowed to keep the points and the position.
Red Bull Racing's Dutch driver Max Verstappen celebrates winning the Austrian Formula One Grand Prix in Spielberg on June 30, 2019. - Max Verstappen won the Austrian Grand Prix after overtaking Charles Leclerc's Ferrari in the closing laps with the stewa
Image credit: Getty Images
TOP TEN
KEY MOMENTS
1/71 - Norris, Raikkonen, Bottas and Hamilton slip past Verstappen. Norris and Hamilton battle it for third, with Bottas taking second. Even Gasly has taken Verstappen now, and Leclrec extends his lead unencumbered. Raikkonen is attacking Verstappen now. Bottas in second.
5/71 - Verstappen is complaining about his car's battery malfunctioning - calling it 'clipping' and perhaps explaining his poor start.
22/71 - Vettel came in to hold up Bottas, who both stopped in the pits for their tires, but Vettel's stop was 6.5 seconds, and Bottas was around half that, which made it all a bit of a wash.
30/71 - Hamilton is going to pit to change his front wing. A tire-only pitstop is a few seconds, this one is 11. He makes his way down the exit, Vettel takes him, as does Bottas and Leclrec. He's fifth.
Charles Leclerc of Monaco and Ferrari during the F1 Grand Prix of Austria at Red Bull Ring on June 30, 2019 in Spielberg, Austria
Image credit: Getty Images
69/71 - Verstappen is ahead! Three laps left, and he's taken almost all of the race to improve upon his lap. Verstappen and Leclerc nudge one another into the corner, and Leclerc is outraged.
71/71 - VERSTAPPEN WINS! A dramatic and brilliant victory, but there is a stewards' investigation to come... There could be late drama here. Bottas in third, Vettel fourth, and Hamilton in fifth.
/dnl.eurosport.com/sd/img/placeholder/eurosport_logo_1x1.png){kind=logo}
/origin-imgresizer.eurosport.com/2019/06/30/2629063-54403950-2560-1440.jpg)
/origin-imgresizer.eurosport.com/2019/06/30/2629065-54403990-2560-1440.jpg)
/origin-imgresizer.eurosport.com/2019/06/30/2629066-54404010-2560-1440.jpg)
/origin-imgresizer.eurosport.com/2019/06/30/2629070-54404090-2560-1440.jpg)
/origin-imgresizer.eurosport.com/2019/06/30/2629071-54404110-2560-1440.jpg)