City have now beaten West Ham in 15 of their past 16 home Premier League encounters, and the Hammers are now without a win in 19 matches against this particular opponent, which is an unwanted club record.
Lopetegui is not responsible for that tale of woe but he wouldn't need to be to know even an off-form City did not need presents.
Yet that is exactly what keeper Areola gave them in the final minute of what had been an encouraging opening period to effectively kill the visitors' hopes of getting anything out of the contest.
Savinho's left-wing cross was excellent, but it was obvious it was going to the far post. Inexplicably, Areola, in a central position, started to come for it even though there was no chance of him getting there.
The former PSG man, 31, checked himself after a couple of strides but by then it was too late. Haaland had an open goal to head into.
It was an outcome that would have compounded West Ham frustrations after Soucek, named skipper as Jarrod Bowen begins his recovery from a broken foot, turned an excellent chance wide after he had been picked out by Mohammed Kudus.
In addition, there was incredulity from the Hammers bench when referee Michael Salisbury blew for a foul by Summerville on Manuel Akanji when it seemed last season's EFL player of the year had merely capitalised on the City defender taking too much time deciding where to pass the ball.
Without Salisbury's intervention, Summerville would have been clean through. Lopetegui was furious. Guardiola's reaction, to look down and rub his head, was a strong hint he felt his side had got away with one.
Haaland made sure City extracted maximum advantage.