Joel Matip's header gave Liverpool the points from a tough assignment at West Ham, where they had fallen behind early on.
Lucas Paqueta fired home after a superb Hammers move to put the hosts ahead after 12 minutes, only for Cody Gakpo to drive Liverpool level from distance soon after.
Diogo Jota missed two excellent chances to put Liverpool ahead in the first half, before Jarrod Bowen had a goal ruled out by VAR for the hosts.
Matip then planted home a fine header from Andy Robertson's corner for what proved to be the winner, although West Ham pleaded for a penalty for what they saw as a handball against Thiago Alcantara late on.
Here are the game's talking points.
1. Liverpool stand and admire Lucas Paqueta's Brazilian brilliance
It was a superb goal that gave West Ham an early lead, as a flowing move ended with Paqueta swapping passes with Michail Antonio and firing home, but it was no wonder that the strike made Jurgen Klopp cut such an angry figure.
Liverpool were guilty of standing off the Hammers as they attacked down their left, and there could also be question marks over Virgil van Dijk who stood off Paqueta as he shot, and even Alisson as the ball didn't exactly nestle in the corner of the net.
Take nothing away from the Hammers though, it was a vibrant start and a goal that showed all the good that Paqueta can do, and there is plenty of that.
He could be a real star in the Premier League next season after this campaign of settling in.
2. Cody Gakpo and Liverpool's powers of recovery
Liverpool conceded twice to Nottingham Forest on Saturday and on both occasions they responded with a goal of their own within four minutes, eventually winning the game 3-2.
It took a little longer here, with Gakpo's strike from distance hitting the net six minutes after Paqueta's did, but it again showed a level of resilience that has been missing from this Liverpool side for the vast majority of their season.
Far too often they've slumped their shoulders and borne the weight of the world on them when things haven't gone well, but the recovery would have pleased Klopp again here, and it led to a sustained period of Reds pressure throughout much of the first half, with Jota guilty of missing two good chances.
3. Trent Alexander-Arnold the centre of attention
This was another game in the roving role for Trent Alexander-Arnold, and it is a position which seems here to stay.
On the one hand Liverpool look better and much more creative going forward when a player of such gifts is given a passport to the centre of the action, but there is a tendency to leave themselves open while they play this way, and that is something that teams who have more going forward than West Ham do would probably have exploited in the first half.
Tweaks to the system are still needed, and the absence of Ibrahima Konate on the right of defence was a big one in that sense, but it is an experiment they'll persist with.
4. Does John Henry need to buy one fewer midfielder?
There was another Liverpool start for Curtis Jones, and another impressive one at that.
After a season and frustration and fairly inconvenient and times downright odd injuries, Jones has returned to the side in recent weeks and provided the sparkle that his supporters know he can.
With John W Henry in attendance at his first game since last year's Champions League final, the young Scouser might just have sent a reminder that the midfield rebuild doesn't have to be as large as many think.
5. West Ham run out of gas, but they've got enough in the tank
It has been a long old season for West Ham, and there is still plenty of it to go with the Europa Conference League semi-finals on the horizon.
Not much of their season has been pleasant given how close they have been to real danger, but the quality within the ranks is clear and there was always likely to be three worse teams than them in this division, something that they showed again here despite the result.
The Hammers appeared to lose energy from the moment Bowen saw his goal chalked off by VAR, and that is no surprise given the efforts they've put in during this campaign.
6. Three on the spin for steadying Liverpool
So that's three wins win a row for Klopp's side, who have improved ever since their struggles in the opening 35 minutes or so against Arsenal earlier this month.
Is it enough to gatercrash the Champions League places? The odds would still suggest no, but they are winning games they simply weren't doing earlier this season, with Matip's header also vanquishing the curse of their horrendous away kit this season. It now has its first win.
That it has taken until the end of April is another, much longer, conversation.
