Liverpool were held in check for most of the first half by West Ham but an own-goal just before the break and a second half barrage proved too much for the Irons. Luis Suárez scored twice for the Reds and Kevin Nolan was sent off after receiving a straight red card late in the match.
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Best chance in the opening ten minutes of the match came from West Ham, despite Liverpool being the better of the two sides. In the 9th minute Mohamed Diame curled a cross into the center of the Liverpool area where Modibo Maíga had snuck behind his defender. But Maíga couldn't connect cleanly with the ball and failed to get a good shot on frame.
Liverpool responded immediately on the counter but Luis Suárez was thwarted by a nice save from Jussi Jaaskelainen.
Maíga again caused problems for the Liverpool problem in the 22nd minute, showing a knack for getting the better of his defender. This time Matt Jarvis found the striker with a cross and this time his header was on target. Fortunately for the Reds, goalkeeper Simon Mignolet was there to touch the ball away with an excellent reflex save.
Liverpool came close in the 41st minute when Raheem Sterling ran onto a splendid ball from Philippe Coutinho. Sterling was able to muscle off his defender but his shot rolled just wide of the far post. One minute later Suárez was again denied at point blank range by Jaaskelainen but the rebound hit off Guy Demel and bounced back into the empty net to give the home side a 1-0 lead at the break.
Liverpool wasted little time extending their lead as the second half opened. After Suárez earned a free kick in a dangerous spot, Steven Gerrard curled the ball towards the far post where Mamadou Sakho got just enough on the ball with a bit of a clumsy effort, to send it over the line. Initially it appeared James Collins might have been guilty of an own goal as he tried desperately to clear the ball, but it was clearly heading over from Sakho's effort.
But not all was well for Liverpool as captain Steven Gerrard limped off in the 56th minute with apparent discomfort in his left hamstring. Lucas Leiva replaced him.
West Ham pulled themselves back into the match, with a little help from Martin Skrtel in the 66th minute. Jarvis' header back across the face of goal from a cross created the trouble and Skrtel, attempting to block the back away from getting to an Irons player, directed it right past Mignolet to make it 2-1.
After some nervy minutes the Reds struck back to put the finishing touches on a victory. Glen Johnson's lifted a cross towards the far post from the right side that floated over Collins' head and met Suárez for the fairly pedestrian header finish to extend Liverpool's lead back out to 3-1.
Less than a minute later West Ham's captain Kevin Nolan was shown a straight red for a needless and stupid challenge against Jordan Henderson. For reasons known only to Nolan, he charged down Henderson from behind and raked his studs on the back of his leg.
Suárez decided to quickly take advantage of the sending off and scored his second goal of the match in the 84th minute. Suárez twisted and turned on the edge of the Irons box to create space and launched a shot that deflected off O'Brien's back, changing direction and leaving Jaaskelainen frozen and the Reds in front 4-1.
Liverpool: Mignolet, Johnson, Sakho, Skrtel, Flanagan (Kelly 79'), Gerrard (Leiva 56'), Coutinho, Henderson, Allen, Sterling, Suárez
Goals: Medel (42' o.g.), Sakho (47'), Suárez (81'), O'Brien (84' o.g.)
West Ham United: Jaaskelainen, McCartney, Tomkins (O'Brien 56'), Collins, Demel, Nolan, Jarvis, Noble, Diame, Downing (Cole 46'), Maíga
Goals: Skrtel (66' o.g.)