The visitors started the game the brightest as Tomás Soucek came close to putting the Hammers in front, only for Alisson to deny him with a superb save down to his right.
The Reds looked most threatening on the break, and so it showed when Luis Díaz broke down the left flank before playing a dangerous ball into the box from which Mohamed Salah won and subsequently scored a penalty in the 16th minute.
West Ham remained dangerous as they looked to play direct crosses into the penalty area, and they finally got their reward as Jarrod Bowen's precise header went in off the post to level the score as half-time approached.
Darwin Núñez should have reinstated Liverpool's lead after half-time after blazing an effort off target, but he made no mistake with his next chance as he volleyed home a ball that was played perfectly over the top of the defence by Alexis Mac Allister.
Manager Jurgen Klopp was happy to see his side finish the game off in the 85th minute as Virgil van Dijk nodded a corner back into the six-yard box for substitute Diogo Jota to tuck away from close range.
Liverpool remained patient in their approach against a defensive West Ham set-up and created plenty of chances to give themselves the best opportunity to win the game. The Reds also defended set pieces well, with some dangerous deliveries put in by dead-ball specialist James Ward-Prowse.
Liverpool conceded too many chances to West Ham and were eventually punished when Bowen's header was directed past Alisson. The Reds must ensure they start the game better, as they could have found themselves a goal or two down on another day.
Manager rating (1-10; 10 = best)
Jurgen Klopp, 8 -- Liverpool's approach was more patient than usual in this game, and that saw a confident Liverpool side look assured in their approach. His decision to start with Nunez was also rewarded with a goal at a crucial time in the game.
GK Alisson, 8 -- Liverpool would have found themselves 1-0 down early on but for Alisson's excellent save against Soucek, but there was nothing he could do about Bowen's header. A reliable performance that kept his side in the game when they needed him.
DF Andy Robertson, 6 -- Worked hard to support attacks down the left flank, but didn't find his intended target enough with his crosses into the box. Made a key intervention in the 73rd minute as West Ham looked to threaten on the break.
DF Virgil van Dijk, 8 -- The Liverpool captain enjoyed a physical battle with West Ham striker Michail Antonio and was dominant in his aerial duels. Organised the defensive line well after they started the game slowly. Assisted Jota's goal to help put the game out of reach.
DF Joël Matip, 7 -- Confident on the ball and made the right decision when venturing forward into advanced areas. A strong second half saw Matip alert, anticipating when direct balls were about to be played into a dangerous area.
DF Joe Gomez, 6 -- The 26-year-old defended well down the right, and he tried to make a difference going forward with crosses toward the back post.
MF Alexis Mac Allister, 7 -- The Argentina international dictated play at the base of midfield to set the tempo of the game, but his moment of the match came with a sublime assist for Nunez's goal on the hour mark.
MF Curtis Jones, 6 -- Took care of the ball and helped maintain Liverpool's dominance in possession. Showed his strength when pressed aggressively and had the ball in the back of the net close to the break, but was marginally offside.
MF Dominik Szoboszlai, 7 -- Always looked to play progressively and was unlucky not to finish the first half with an assist for Jones after a precise clip to the back post. Linked up well with Salah in Liverpool's more patient attacking phases.
FW Luis Diaz, 6 -- The Colombia international challenged his marker directly but often found himself crowded out by multiple defenders. Usually made the right decision against a stubborn back line.
FW Darwin Nunez 8 -- Astute runs in behind stretched the West Ham defence, and it was the Uruguay international's run that led to Salah winning the penalty for the opening goal. Should have scored with his strike in the 53rd minute that he blazed off target after some impressive build-up play from Liverpool, but his well-timed run and clinical volley to give Liverpool their lead back more than made up for it.
FW Mohamed Salah, 7 -- A constant threat in attacking areas and linked well with Nunez. Won the penalty for Liverpool's opener and dispatched it with power.
Substitutes (players introduced after 70 minutes get no rating)
Cody Gakpo (Nunez, 81') N/R -- Got involved quickly when introduced with bright hold-up play. Almost played in Salah for a chance, but put a little bit too much on the pass.
Diogo Jota (Diaz, 81') N/R -- Found his way onto the scoresheet in a matter of minutes as he connected with Van Dijk's flick-on to give Liverpool a two-goal cushion.
Wataru Endo (Mac Allister, 88') N/R -- Brought on to help see the rest of the game out.