The pair picked up punctures as they scrapped for the race win inside the final 10 laps, effectively ending their races – quite literally for Norris.
It left Russell out front, holding on from Oscar Piastri with Carlos Sainz rounding out the podium.
A good jump from Verstappen saw the Dutchman hold the lead from Norris, who came under pressure from George Russell into Turn 3.
The McLaren driver held on, Russell slotting into third from Lewis Hamilton with Sainz in fifth ahead of Sergio Perez.
Oscar Piastri was pushed wide by the Mexican exiting Turn 4, kicking up the gravel and losing a spot to Charles Leclerc.
The Ferrari driver then had a moment at the following corner, the result of a broken front wing, and fell back behind the Australian, pitting at the end of the lap.
By the time DRS was enabled at the start of Lap 2, Verstappen was out of range of Norris in second.
The two Mercedes drivers swapped positions at Turn 3 on Lap 3, Russell losing out before using DRS to regain the place into Turn 4.
Having attacked his team-mate, Hamilton dropped back and soon came under pressure from Sainz.
The Spaniard slipped up the inside into Turn 3 to take fourth on Lap 6 as the Mercedes driver ceded the position – Hamilton had been under investigation for leaving the track and gaining an advantage at the start.
Behind them, Piastri made the move beyond Perez on Lap 7 with a bold move around the outside of Turn 5, the first of the two long left-handers in the middle of the lap.
Having fallen to 12th in the early stages, Daniel Ricciardo pitted and the end of Lap 10, swapping from the medium rubber onto a set of hards.
The white-walled rubber had shown similar pace to worn mediums on the leaders, Leclerc having swapped onto a set at his Lap 1 stop.
Verstappen had stretched the race, pulling 5.5s clear of Norris after 15 laps, with Norris 3.9s back in third.
Piastri remained sixth, 15s away from the lead Red Bull Racing and two seconds back from Hamilton in fifth.
A second stop for Leclerc on Lap 17 saw him feed out just in front of the race leader, his hard compound tyres only lasting 16 laps as he swapped back onto the medium tyres.
There was a mix of strategies being employed, with some having moved onto a three-stop while others continued beyond Lap 20, more online with Pirelli’s expected primary strategy.
Hamilton and Perez were the first of the front runners in the lane at the end of Lap 21, the Mercedes driver catching the eye of officials for potentially crossing the white line at pit entry courtesy of an armful of oversteer as he peeled into the lane.
The leaders were in on the following lap, Piastri remaining on track to inherit the lead before his own stop on Lap 25.
A quick decision from officials saw Hamilton handed a five-second penalty for crossing the white line on pit entry, Fernando Alonso having also been pinged but his for contact with Guanyu at Turn 3 earlier in the race.
They then moved to investigate Verstappen for an unsafe release from his pit box after appearing to baulk Norris, though nothing came of that incident.
Following the opening round of stops, Verstappen led from Norris, Russell, Sainz, Hamilton, Piastri, Perez, Nico Hulkenberg, Kevin Magnussen, with Daniel Ricciardo rounding out the top 10.
Perez was the latest to cop a five-second penalty after he was found speeding in pit lane.
At half-distance, Verstappen was 8.3s clear of Norris, with Russell 6.3s further back in third.
Piastri remained sixth, 24s away from the front of the race, with Ricciardo holding on to the final points-paying position.
The RB driver served his second stop on Lap 37, dropping from 10th to 16th as he had another set of hard tyres fitted.
Russell triggered the second round of stops for the leaders when he boxed after 46 laps.
Mercedes hauled him in as he encountered a gaggle of traffic, a group that proved troublesome for Verstappen in the lead as a stop at that point would have seen him emerge in that group.
The race leader had lost time to Norris as he worked through the traffic, his advantage eroding to 6.4s but soon extending once he was through the other side of the backmarkers.
On track, Piastri picked off Hamilton on Lap 49, moving up the inside at Turn 3 to take third before enjoying a helping of DRS in the run to Turn 4 to hold the position.
Having become increasingly vocal over the state of his tyres, Red Bull Racing called Verstappen into the lane on Lap 51.
Norris followed him in, McLaren making up time in the stops to effectively halve the deficit to the Dutchman ahead.
Piastri stopped soon after, falling to sixth but rejoining in clear air.
The second sequence of stops was completed by Hamilton stopping on Lap 54, coinciding with Norris latching on to the back of Verstappen for the race lead.
The McLaren was in DRS range, looking up the inside at Turn 3 and forcing the leader to defend the move on Lap 56.
The order remained Verstappen from Norris, though by less than a second, with Russell third ahead of Sainz and Piastri.
Hamilton ran sixth after serving his penalty at his second stop, then came Hulkenberg, Magnussen, Perez, and Ricciardo.
With 15 laps remaining, Verstappen complained of a lack of grip as Norris received the black and white flag for exceeding track limits for a third time.
The pair remained locked together, the McLaren shadowing the Red Bull Racing ahead as the pair ebbed and flowed while managing their energy reserves.
On Lap 59, a late move from Norris at Turn 3 saw him skate up the inside but off the road, handing the position back to Verstappen on the run to the next corner.
It was an ambitious move, the front wheels smoking as he tried to round the tight right-hander, breaching track limits for a fourth time as a consequence, a point noted and then investigated by officials.
Norris tried again on Lap 61, this time into Turn 4, when he was forced by Verstappen to the outside, where there was no way through.
It was a frantic battle, Verstappen doing all he could to hold on from a McLaren that was clearly faster but could find no way through.
Another late move from Norris on Lap 63 saw Norris nose ahead at Turn 3 but the leader ran off the road at the exit to maintain position.
Next time around, the pair made contact at Turn 3, puncturing Verstappen’s left-rear. Norris too picked up a puncture as Russell inherited top spot.
Rubbing salt into the wound was a five-second penalty for Norris who ultimately retired from the race as he returned to the pits.
For his part in the clash, Verstappen was given a 10-second time penalty, the Dutchman running fifth after he’d limped back to the pits.
The front of the race was Russell from Sainz and Piastri, the Australian moving into second on Lap 65, driving around the outside of Sainz at Turn 5.
Russell held a 2.8s advantage over the chasing McLaren but not making inroads quickly enough as the laps ticked down.
The Mercedes driver held on to win by less than two seconds after 71 laps of racing ahead of Piastri, with Sainz third ahead of Hamilton, Verstappen, Hulkenberg, Perez, Magnussen, Ricciardo, and Pierre Gasly rounding out the points.