Liverpool's chances of making it nine games without defeat had been buoyed by the return of club captain Steven Gerrard from a groin injury.
Key to that sequence of results had been the Reds' ability to keep opposition attackers at bay, with Pepe Reina tallying five shut-outs in six games. Kenny Dalglish opted to field three centre-backs in a bid to maintain that miserliness, including 19-year-old Danny Wilson, who found his name on a Barclays Premier League teamsheet for the first time.
Another notable inclusion was the man who now wears No.7 at Anfield, Suarez. The Uruguayan set about making an instant impact on two minutes with an audacious lob into the box which was just too heavy for the onrushing Gerrard.
West Ham countered with a stinging drive from Thomas Hitzlsperger which Reina managed to contain before Gerrard plonked a fabulous ball onto the head of Raul Meireles, who succeeded in nodding it over Hammers custodian Robert Green only to see his effort drop wide of the post.
The bright start continued with an angled whack from Meireles on 12 minutes which proved comfortable for Green, while Johnson attacked a corner before seeing his header cleared as it flew towards the net.
Liverpool, then, had looked the more likely but it was the hosts who took the lead in style on 22 minutes when Parker masterminded a one-two with Hitzlsperger before arrowing past Reina.
The Reds sought to level immediately when Suarez broke into West Ham territory before laying to Dirk Kuyt. The Dutchman cut inside and lashed a 25-yard shot into the side netting.
Avram Grant's charges were not resting on their laurels, however, and could have got a second when Frederic Piquionne flashed a ball across the face of goal that was inches away from the slide of Demba Ba.
Liverpool's next opportunity came from an unlikely source: Martin Kelly cutting in from the right before driving into the grateful arms of Green. Minutes later the defender stormed down his flank once again before collapsing to the turf clutching his left hamstring.
It was immediately obvious a substitution would be required, and Dalglish chose to make it an attacking one: Joe Cole coming on to face his old club. He would operate on the left in what would now be a 4-4-2.
The new shape had barely had chance to set when West Ham doubled their advantage, Gary O'Neil crossing for an unmarked Demba Ba to head home seconds before the half-time whistle.
Dalglish acted again four minutes into the second period, introducing David Ngog for the limping Meireles.