Brendan Rodgers' men made it back-to-back wins in the league for the first time this season and leapfrogged above the Hammers - but they had to come from behind late in the game to do so.
Glen Johnson put them into the lead after just 10 minutes when he produced a goal-of-the-season contender from the edge of Jussi Jaaskelainen's penalty area.
Mark Noble slotted from the spot after Joe Allen was adjudged to have handled in the penalty area before Steven Gerrard turned a Matt Jarvis cross past his own 'keeper to give West Ham the lead.
However, Joe Cole struck against his old club to equalise and then Collins turned a Jordan Henderson cross into his own net to send the travelling Reds into euphoria.
All the build-up to the clash revolved around the absence of Luis Suarez, who was ruled out after picking up his fifth yellow card against Southampton, but his replacement Shelvey proved to be the hero of the hour.
Upton Park was on its feet on six minutes when Jarvis's cross was scrambled clear by Daniel Agger and Mohamed Diame fired the loose ball against Carlton Cole, who deflected it a yard wide of Pepe Reina's post.
The Hammers posed a real threat down the left flank with Jarvis, who was constantly keen to spin a deadly cross in behind Martin Skrtel and Agger and this would prove to be a real thorn in the Reds' side throughout the match.
Full report: Liverpool FC Official
Fabio Borini netted his first Liverpool goal as the Reds clinched a place in the Europa League play-offs with a 3-0 win against FC Gomel.
With Liverpool stuttering with draws at home and Chelsea’s recent poor form, this match was vital for both teams to get a positive result so they keep in touch with the leading group. Liverpool have had good results against Chelsea in recent years and they managed to do the double over them last season. Dalglish is unbeaten as manager against Chelsea so confidence was good going into the match.
Dann was a player who was definitely tipped to be heading to the Premiership after Birmingham City were relegated at the end of last season.
Aly Cissokho could become the answer to Liverpool's left-back problems after Lyon revealed they are willing to listen to offers.
The defender committed himself to the Reds by putting pen to paper on the deal at Melwood on Wednesday afternoon - and then explained to us why he had no hesitation in doing so.
Goals from Scott Parker and Demba Ba had the Hammers looking comfortable before a late strike from Glen Johnson gave the Reds hope.
It has been suggested Liverpool would be willing to listen to offers for Johnson with the England international believed to be unsettled on Merseyside but Hodgson denied claims Glen Johnson would be offloaded in January, and insisted the new owners were looking to build the team long-term, and the club would spend sensibly.
Real Madrid are prepared to pay Liverpool 
Moores, whose family became one of the richest in Britain with the creation of the Littlewoods empire, took the role of chairman in 1991.
The Blues doesn’t want the England international fullback who played for Chelsea between 2003-2007 sign for their arch-rival. Chelsea sold him to Portsmouth for £4million back in 2007 will need to forked out £13.5million extra to get him back.
Still no news on the transfer front from Liverpool after the club made an official statement that they are not going for Spanish players as suggested in the press’ speculation.
