An explosive end to the first half saw Guy Demel tap home an equaliser after Steve Gerrard had scored a minute earlier from the spot.
James Tomkins handled a Luis Suarez attempted ball through and Gerrard sent Adrian the wrong way.
But a new and composed Irons went straight down the other end and from a corner scored in a moment of controversy.
Ref Anthony Taylor ultimately over-ruled his assistant who claimed Andy Carroll had fouled keeper Mingolet to send the home side in level.
Boss Sam Allardyce – defying all the critics – sent out his team to play with a new freedom – and the Hammers more than deserved their share of things at the break.
In a 45 minutes of few chances, they dominated for long spells, never allowing the visitors to truly hit their stride.
They survived an effort from Suarez – a delicate chip – which hit the bar midway through the half and played with plenty of style.
Mark Noble saw a free kick fly wide and Mo Diame turned well to let fly with a wild effort before the game took off with the two goals inside a minute.
There was no doubting the Liverpool pen when Tomkins handled but the equaliser came about after TV replay appeared to show that AC had an arm in the keeper’s face.
Taylor however remain unimpressed and after a long debate gave the goal which no one could say we didn’t deserve.
Pablo Armero at left back was impressive, growing into the game more and more as the half developed.