Anyone who thinks that protest will derail West Ham’s efforts to stay in the Premier League should probably pipe down now. Far from affecting performances on the pitch, the atmosphere generated by the biggest demonstration yet against David Gold, David Sullivan and Karren Brady seemed to bring the best out of West Ham, who rose to the challenge by climbing out of the bottom three with this an emphatic victory.

This was a rare good day for West Ham, who are up to 16th after their first league win since New Year’s Day. “Support the team not the regime,” was the message from Hammers United, the fan group organising the protests, and there was no sign of any toxicity inside the London Stadium. Although supporters voiced their disapproval with the board outside the ground, there was nothing but positivity once they were in their seats and the team responded in style.

West Ham, who have played a game more than 19th-placed Aston Villa, can be confident of staying up if they maintain this level. There is quality in this team; weapons at David Moyes’s disposal. He has options in attack and he put them to good use here, easing the pressure with a triumph built on the power of Sébastien Haller and Michail Antonio up front, Jarrod Bowen’s first goal since his £22m move from Hull in January and two neat assists from Pablo Fornals. “They’ve done a great job,” Moyes said. “All of them contributed. The crowd were great. The team also helps.”

West Ham fans displeasure with the board took many forms during their demonstrations outside the London Stadium. Photograph: Tom Jenkins/The Observer

The focus before kick-off was drawn to an estimated 3,000 supporters marching against Sullivan, Gold and Brady. It started in Plaistow, a short walk from where Upton Park once stood, and it was hard to find anyone with a good word to say about the people running this troubled club. There were GSB Out banners and T-shirts, there were GSB Out stickers pushed on to lamp posts and it was clear from the fiery speeches and the mutinous chants that supporters have completely lost faith with those at the top.

There was humour, too. A Southampton fan emerged from Pudding Mill Lane station and asked if she was really supposed to be looking at a football ground. “No, it’s an athletics stadium,” a police officer replied.

It all passed peacefully and there was a good atmosphere inside the ground. West Ham were up for it after coming close to nicking a point at Liverpool last Monday and, for all the complaints about Moyes being too negative, there was an adventurous look to the Scot’s 4-4-2 system. Haller was back in the side and the £45m striker’s physical partnership with Antonio was highly effective. “We could never defend them in a way we should do in the Premier League,” said Ralph Hasenhüttl, Southampton’s manager.

There were also plenty of bright touches from Bowen on his first start for his new side, including a cheeky nutmeg to embarrass Ryan Bertrand, and he opened the scoring in the 15th minute. The impressive Declan Rice won possession in midfield and when Fornals spotted Bowen making a run from right to left, the Spaniard’s pass allowed the winger to dink a lovely finish over Alex McCarthy with his left foot. Perhaps Moyes was right to ease the 23-year-old in gently. “I know a little bit about bringing in the boys from the lower leagues at the right moment,” he said.

Haller spurned a chance to double the lead, heading straight at McCarthy, and Southampton stirred after a lethargic start. When the visitors exposed Mark Noble’s lack of pace in midfield with a slick counterattack in the 31st minute, Stuart Armstrong found James Ward-Prowse and his cutback gave Michael Obafemi the chance to curl a shot beyond Lukasz Fabianski.

Michail Antonio wheels away in celebration after slotting home the Hammers’ third goal. Photograph: Tom Jenkins/The Observer

The confidence briefly seeped out of West Ham, who have lost 22 points from winning positions this season. Yet there was something different about them here; more defiance, a greater sense of purpose. They should have regained the lead when Issa Diop produced an absurd miss, ducking underneath Aaron Cresswell’s corner, and they did regain the lead when an error from McCarthy gifted Haller his seventh goal of the season. Antonio sliced a cross into the area from the left and the Southampton goalkeeper was far too tentative as he came to collect, allowing Haller to bump him with a legal challenge, nod the ball away and turn it into the empty net.

There would be no VAR reprieve for McCarthy and West Ham scored again in the 54th minute, Haller flicking on for Fornals to release Antonio, who finished with aplomb.

Southampton introduced Danny Ings but Haller almost created another goal for Antonio with a rabona. West Ham saw the gloom lifting.