The Reds came into the game just one goal shy of the illusive 100 goal mark, Liverpool ensured that they surpassed such a tally in style - only once in their Premier League history have they done so in fewer matches (2013/14).
The Reds on the day moved up to second in the table with the victory, which was started by Emre Can’s deadlock-breaking header midway through the first half.
Mohamed Salah then grabbed goal No.31 of the season and counting after the break before Firmino netted.
Hammers substitute Michail Antonio made an impact after coming off the bench to reduce the deficit, but Sadio Mane’s close-range finish from an Andy Robertson cross sealed the win.
The win moved the Reds to second, however, Manchester United's 2-1 win against Chelsea on Sunday saw the Red Devil's leapfrog, Liverpool, to return to the Runners-up position.
Afterwards, Klopp was enthused about the manner of his side’s display against a West Ham team who arrived at Anfield in decent form since the appointment of David Moyes who has steadied the ship in east London after the sacking of Slaven Bilić back in November 2017.
After speaking to the press Klopp went on to say how impressed he was with his team's win stating: "I am really happy with the complete performance, all the individual performances were really, really good today.
"When we had problems in one or two moments, we had comebacks in the game and then didn’t suffer or whatever. It was just a good game and we were really difficult to play today, I would say.
"We scored fantastic goals and created a lot more chances and that’s against a David Moyes team - really good organised, in a good moment in the league, good quality, individual quality.
"So today I have nothing to criticise, to be honest", the German manager added.
Salah equals Luis Suarez' best ever tally in a season for Liverpool
Mohammed Salah has been one of the stand out performers in the 2017-18 Premier League season and the 25-year-old scored for a sixth successive game on Saturday as the former Chelsea man equalled Luis Suarez' best ever goal tally in a Redshirt.
The Egyptian netted his 31st goal of the season in a move that was brilliantly assisted by Oxlade-Chamberlain who bullied his way through the West Ham midfield before prodding the ball through to Salah. From then on there was only one outcome as Salah slotted his 20th left-footed strike of the season to continue his stunning form upon his return to England's top-flight.
His manager Klopp could not keep quiet his admiration for the Reds star man this season: "In football, it is all about doing the right thing in the right moment. I like Mo’s desire for goals
"Flexibility and being fluent depends on all the players around, it cannot only be one player who is flexible and fluent because it doesn’t help.
"If you see how we change positions, how Roberto immediately defends each moment for Mo when Mo is in this situation, Sadio is doing the same, it’s really important.
"He is obviously doing well and it was not the biggest chance we had in the game from which he scored from. It was a nice goal", Klopp continued.
Liverpool will resume training today with their sights set on their fixture with Newcastle United at Anfield on Saturday evening. The fixture also see's the arrival of much-loved Champions League-winning former Reds manager Rafael Benitez who returns to Merseyside this weekend.