The job security of both Lopetegui and O'Neil was one of the two dominant storylines before kick-off in a match dubbed 'El Sackico' on social media.
The other was the health of Michail Antonio, who is currently recovering from a serious car crash.
In a tense first half, the Hammers could have done with the finishing power of their all-time leading Premier League goalscorer, who was given a show of support by both the club's players and fans, before and during proceedings.
Bowen, Carlos Soler and Mavropanos all had opportunities to open the scoring for the hosts but were unable to break the deadlock against a determined Wolves, who came into the contest having conceded more goals than any other top-flight side.
However, Wolves' resistance was broken eight minutes with their Achilles heel - defending from corners - proving costly again as they shipped their eighth goal of the campaign from one.
Even in those circumstances there was a huge element of misfortune. Wolves' captain Mario Lemina was convinced the ball went out off Aaron Wan-Bissaka before the corner was awarded, and subsequent replays showed it did.
Lemina's frustration visibly boiled over at full-time when he was involved in a heated confrontation with Bowen, which resulted in a booking and other players dragging him away from the England forward.
The visitors will justifiably feel aggrieved by further decisions that went against them.
West Ham, whose last home victory over Manchester United also came after they were awarded a penalty that should not have been given, will be delighted to have enjoyed the rub of the green again in potentially pivotal fixture.