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Verstappen won from his Red Bull Racing team-mate Sergio Perez and Charles Leclerc while Bearman rose from 11th to seventh and points on his F1 debut.
Oscar Piastri was fourth while Daniel Ricciardo came home 16th after a slow pit stop and a late spin in the RB.
From the race start, Verstappen maintained the lead into the first corner, sweeping across the road to defend against Leclerc, who held second from Perez.
Having maintained 11th off the line, Bearman attacked Yuki Tsunoda at Turn 13 on the opening lap. He couldn’t make it work there and attacked again off the final corner.
On the formation lap, Pierre Gasly reported a gearbox problem in the Alpine, the Frenchman instructed to retire the car at the end of the opening lap.
Piastri had risen from fifth to fourth at the start, moving around the outside of Fernando Alonso to claim the place.
At the end of the opening lap, Verstappen headed Leclerc, Perez, Piastri, Alonso, Lando Norris, George Russell, Lewis Hamilton, Lance Stroll, and Tsunoda, while Ricciardo had fallen to 15th.
Tucked up in the slipstream as they ended Lap 2, Perez pulled out and eased up the inside of Leclerc to take second place.
Running ninth, Stroll found the wall at Turn 23 to end his race and draw the Safety Car.
The Canadian had brushed the apex barrier at Turn 22, which careered the Aston Martin across the road and into the barrier at Turn 23.
Much of the field pitted, Red Bull Racing double stacking Verstappen and Perez but servicing both without delaying the latter.
McLaren elected not to stop Norris while Mercedes took the same decision with Hamilton, while Nico Hulkenberg and Zhou Guanyu were the only others not to head in.
That left the order Norris from Verstappen, Russell, Hamilton, Perez, Leclerc, Piastri, Alonso, Hulkenberg, Russell and Zhou.
The sequence was disastrous for Ricciardo, who slipped to 18th, the last runner on track, after a slow RB stop.
Leclerc also lost ground, Ferrari holding him in the pit bay as traffic in the lane prevented his exit.
Racing resumed at the start of Lap 10, Norris maintaining the lead into the first corner while Piastri attacked Leclerc for fifth but couldn’t make it stick.
In the pack, Kevin Magnussen and Alex Albon made contact as the Haas driver squeezed the Williams towards the barrier, leaving Albon with nowhere to go.
The clash, which caught the eye of officials, left Magnussen reporting floor damage while Albon too sustained damage in the clash.
Verstappen reclaimed the race lead at the start of Lap 13, using DRS to breeze by Norris.
Behind them, Hamilton fell victim to Perez, who moved into third as they braked into the opening left-hander.
Officials deemed Perez warranted a five-second penalty for an unsafe release during the Safety Car pit stops while Magnussen was handed a 10-second penalty for his role in the incident with Albon.
Piastri and Hamilton battled into the first corner as they began Lap 17.
The Mercedes driver held his line and pushed the Australian wide, Piastri ducking through the escape road to get ahead but quickly ceded the position back.
It was a scrap that carried on, the McLaren’s lack of top speed making Piastri’s task difficult.
There was more pain for Magnussen as officials slapped him with another 10-second penalty, this time for leaving the track and gaining an advantage as he put a move on Tsunoda.
Having not stopped under the Safety Car, Norris fell victim to Leclerc at the start of Lap 27 as the McLaren driver’s medium tyres began to cry enough.
Outside of the top 10, a five-way scrap for 12th developed between Magnussen, Ocon, Tsunoda, Albon, and Sargeant.
Magnussen was working hard to fend off the pack in service of his team-mate, with Hulkenberg running 10th, to afford the German enough time to serve his pit stop.
Ricciardo and Valtteri Bottas soon joined the pack, the most interesting action on track as, out front, Verstappen was well clear of Perez.
Haas pulled the trigger on Hulkenberg’s stop at the end of Lap 34, rejoining the race in 11th – a net 10th as Zhou ahead was yet to stop.
Piastri finally got by Hamilton into Turn 1 on Lap 35, but went too deep and ran off the road, handing the place back to his Mercedes rival.
The Australian boxed for a second time at the end of Lap 36, dropping to fifth as he took a second set of hard tyres.
Norris was in next time around, swapping his medium tyres for a set of softs.
He quickly came under the attention of Hamilton, officials warning the McLaren driver for weaving down the front straight.
With every driver having completed their stops, the order was Verstappen from Perez, Leclerc, Piastri, Alonso, Russell, Bearman, Norris, Hamilton, and Hulkenberg.
With a handy advantage over Leclerc in third, even with his five-second penalty, Perez was comfortable on the second step of the podium.
In the final laps, the interest was focused on Bearman’s attempt to see off Norris and Hamilton.
The chasing pair both had new, soft tyres fitted and were reeling in the Ferrari driver.
Bearman’s hopes were raised when Norris came under fire from Hamilton with five laps remaining, the McLaren driver’s soft tyres beyond their best.
Still, Bearman was losing time and sat just 2.8s clear with four laps to go – with Norris closing at around half a second a lap.
Ricciardo had a late spin, clipping too much kerb at Turn 1 which pitched him around on the penultimate lap.
He kept it out of the barrier and didn’t lose a spot, but it was a disappointing end to a similarly disappointing race – compromised by a slow stop under the Safety Car.
There were no such issues for Verstappen as he won once more from Perez, Leclerc third with the bonus point for the fastest lap.
Piastri finished fourth ahead of Alonso, Russell, the incredible Bearman, who’d sensationally resisted the pressure of Norris and Hamilton to take seventh place at the flag, and score world championship points on debut.
Hulkenberg rounded out the top 10 for Haas’ first point of the season.
The result marked Verstappen’s ninth successive race win, the 56th of his career, and 100th F1 podium.
