It was the British driver's second career victory, endorsing the improved form of the Mercedes team in recent races, as he made the most of Verstappen’s impulsive and aggressive move against Norris, to finish 1.9 seconds clear of Oscar Piastri in the second McLaren.
"Incredible!" said Russell, who had registered Mercedes' last win in Brazil in 2022.
"I think it was a tough fight out there at the beginning of the race just to hold on to that third place and I saw on the TV that Max and Lando were getting pretty close -- and I knew Lando would want to try to get that race win.
"The team has done an amazing job to put us in this fight and you've got to be there in the end to pick up the pieces."
Carlos Sainz finished third for Ferrari ahead of seven-time champion Lewis Hamilton in the second Mercedes and Verstappen, who was fifth, despite collecting a 10-second penalty for causing the crash with Norris, who was forced to retire his damaged car.
On a hot day in the Styrian Alps, with air temperatures touching 29 degrees and the track at 49, Verstappen made his now customary flawless start from pole.
Russell also made a good start from third and fought Norris for second on the opening lap.
Verstappen pitted on lap 23, followed by Norris and the rest, passing the race lead to Piastri until he pitted on lap 25. Piastri rejoined sixth and order was restored with everyone on hards, except Russell who took a second set of mediums.
"He launched straight into me – I couldn't turn right into the box," said Norris, complaining about Verstappen's alleged unsafe release by Red Bull.
"Yeah, we’re on it,” came the reply.
By lap 41 Verstappen was grumbling about his tyres.
"I don’t know what’s happening," said the champion who had only a fresh set of hards or used mediums left to run.
10 second penalty
By lap 44, Verstappen’s lead was down to 6.4 seconds before Russell, also struggling, pitted for fresh hards, re-joining sixth. He swiftly set a fastest lap and passed Sainz for fifth behind Hamilton, who was behind the two McLarens.
With the leaders extending their stints to make a two-stop strategy work, back-markers like Leclerc in 12th on three stops were faster on track, but stuck behind Verstappen until he pitted again with Norris on lap 51.
The Dutchman suffered a slow stop due to a ‘sticky’ left rear and Norris on fresh mediums was only 2.2 behind as they rejoined in P1 and P2. Verstappen was on used mediums, delivering the prospect of a thrilling duel to the flag.
Norris was three-tenths adrift before passing him on lap 59, but ran wide and off-track. He gave the position back and received a warning for exceeding track limits before attacking again only for Verstappen to run wide and rejoin.
The battling pair eventually collided on lap 63 at Turn Three where Verstappen moved across to hit Norris’s car and both suffered punctures, gifting the lead to Russell as they limped back to the pits.
Verstappen’s front left was damaged and Norris’s right rear, with sufficient damage for the McLaren to retire as Verstappen rejoined in fifth, only to receive a 10-second penalty for causing the crash which led to a brief Virtual Safety Car.
Nico Hulkenberg came home sixth for Haas ahead of Sergio Perez in the second Red Bull, Kevin Magnussen in the second Haas, Daniel Ricciardo of RB and Pierre Gasly of Alpine.
Leclerc finished 11th in the second Ferrari after a race of four pit-stops following a first lap incident.
