West Ham's recent victory puts them nine points above the relegation zone, ending a three-game winless streak. Meanwhile, Wolves continue to struggle, sitting four points away from safety after suffering their 10th loss in 15 league games.
In the aftermath of last week's 3-1 loss at Leicester, Lopetegui was reported to have survived a board meeting about his position.
But the Spaniard, who replaced David Moyes in the close-season, must build on this valuable victory over the team he managed in the 2022-23 season before he can fully relax.
"I don't talk about noise, I talk about football. If you ask me about football, I will. A win is always good for me," Lopetegui said.
"The fans have supported us a lot through the bad times. I'm happy for them."
O'Neil, who played for West Ham from 2011 to 2013, heard Wolves fans call for his dismissal during their 4-0 thrashing at Everton on Wednesday.
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Now he will anxiously await the verdict from the Wolves board on his future, which looks bleak after the latest blow to Wolves' survival hopes.
"An awful lot of decisions went against us in a big game, big moments. You need some of them to go your way but they didn't," O'Neil said.
"I'm not concerned. People above me are supportive, but the supporters want to be successful. I understand I have to take responsibility."
West Ham were rocked at the weekend by the news that their Jamaica striker Michail Antonio had been in a serious car crash that left him needing surgery on a lower limb fracture.
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The 34-year-old had to be cut out of his Ferrari following the accident, with Lopetegui admitting it was a "miracle" he survived.
"It wasn't an easy week. We dedicate the victory to Michail," Lopetegui said.
Hammers fans held a minute's applause for Antonio in the ninth minute to match his shirt number.
Composed Bowen
That emotional moment was in stark contrast to the turgid first half fare produced by two teams wracked with nerves and undermined by a chronic lack of quality in possession.
Wolves should have broken the deadlock when Matheus Cunha's pin-point pass sent Doherty racing away for a teasing cross that Joao Gomes slashed over from close-range.
It was a costly miss as Soucek put West Ham in front from a 54th minute corner, the unmarked Czech midfielder rising to loop his header over Sam Johnstone from six yards.
O'Neil was fuming again after Wolves were controversially denied a penalty for Emerson's push on Goncalo Guedes.
Doherty gave O'Neil hope in the 69th minute when the defender met Rayan Ait-Nouri's cross with a half-volley that flashed past Lukasz Fabianski from 10 yards.
But Bowen restored West Ham's lead three minutes later as the England forward danced into the Wolves area before guiding a fine finish into the far corner.
On a night when Antonio was never far from West Ham's thoughts, Bowen celebrated his crucial winner by holding aloft his team-mate's shirt.
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In a dramatic finale, Wolves had another penalty claim rejected when Konstantinos Mavropanos tripped Jean-Ricner Bellegarde, before Fabianski denied Mario Lemina to leave O'Neil facing the axe.
(This story has not been edited by staff and is auto-generated from a syndicated feed.)