Although Ian Holloway's team had the better of the early possession, it was the visitors who did more with the ball when they had it, and the first meaningful chance fell to Obinna.
Frederic Piquionne fired in a cross from the left which was allowed to go all the way across the box to Obinna and his bobbling shot drew a good full-stretch from Kingson.
Obinna was a constant threat, and with West Ham having clearly identified the right-hand side of Blackpool's defence as a weakness, he was regularly in the thick of the action.
When the first goal of the game came, it was no surprise that the Nigerian was involved.
He twisted and turned and pulled marker Craig Cathcart out of position, and opened up the angle to shoot from the left-hand corner of the box, with Kingson inexplicably palming the ball into his own net.
Grant happy with impact of new signings
But with the Hammers having shipped 10 goals in their last three league games, Blackpool knew the visitors were open to a sucker punch, and they very nearly landed one through Andy Reid.
The Blackpool debutant spotted keeper Robert Green off his line and tried to curl a shot into the far top corner from wide on the right, but the England keeper back-pedalled and managed to finger-tip the ball over the bar.
Seeing their lead threatened roused West Ham to action and inevitably Obinna was involved.
He drew a fine double save from Kingson but there was nothing the Ghanaian could do about Keane's follow-up volley into the bottom corner from close range.
But just as Avram Grant's side were starting to think of the rare luxury of a two goal half-time cushion, Blackpool struck back.
Adam, the focus of so much pre-match attention, fired in a low corner from the right which somehow eluded everyone and skidded into the far corner to put the hosts on the scoreboard.
Amazingly, there was still time for another goal before the break, and once again, Obinna was at the heart of things.
Holloway determined to entertain despite defeat
Scott Parker charged forward from the centre circle and laid the ball off to Obinna, who unleashed an unstoppable left-foot shot from 30 yards into the top corner.
Adam continued to show his huge value in the transfer market by being at the centre of everything Blackpool did, and he came within inches of narrowing West Ham's lead when he smashed a second-half free-kick against the crossbar.
That free-kick was earned after James Tomkins fouled substitute James Beattie and the introduction of the former Everton striker caused West Ham's defence all kinds of problems.
Winston Reid in particular struggled to deal with him, and was lucky to avoid conceding a penalty when he hauled Beattie down in the box, although the forward did not complain much about the decision.
Beattie came on at the same time as former Hammer Marlon Harewood, showing the home side's attacking intent, and they laid siege to Green's goal for the rest of the game.
But for all Blackpool's pressure, Green's stoppage-time one-handed save from Harewood was one of the few times he was truly threatened, and the visitors held on for only their second away win of the season.
Blackpool manager Ian Holloway:
"To be honest I can't wait to get away from home.
"All these things are happening in front of our own fans and it is not nice.
"So, let's get away, play at Everton on Saturday and see if we can stop the rot."
West Ham manager Avram Grant:
"I am very pleased with how we attacked in the first half - we created a lot of chances.
"In the second half we defended very well, which we didn't do in the last games we were winning against Everton and Birmingham.
"It was a very important win. Every game now is very important for us.
"We wanted to make one step today, we have finished the second third of the league and are starting the last third."
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