But they made no such mistake from a similar position against Atletico Madrid in midweek, winning their fourth straight Champions League match to qualify from a tough group with two games to spare.
Those two results form part of a 25-match unbeaten run which equals a club record first set by Bob Paisley's 1982 side.
West Ham are in a great place too.
Their tally of 20 points in the Premier League is the same as Manchester City's and that's good enough for fourth place in the table going into the weekend.
When, where and how to watch
When: Sunday, November 07, 4.30pm BST
Where: The London Stadium
How to watch: Sky Sports
Last three meetings
West Ham 1-3 Liverpool (January 31, 2021)
After three defeats in their previous five games, Liverpool were in wobbly form but a superb double from Mo Salah delivered a blow to an in-form Hammers side that had won their previous six matches.
Liverpool dominated a goalless first half but then went 2-0 up via two superb Salah strikes, his second after brilliantly controlling a high cross from Xerdan Shaqiri.
Gini Wijnaldum made it 3-0 after being set up by Roberto Firmino before West Ham netted a consolation goal through defender Craig Dawson.
Liverpool 2-1 West Ham (October 31, 2020)
The Reds enjoyed 72% possession but found themselves 1-0 down with 42 minutes gone after Pablo Fornals had given West Ham a surprise lead.
The hosts levelled three minutes before the break when Arthur Masuaku fouled Salah and the Egyptian tucked home the resulting penalty.
With Nat Phillips making his league debut due to the absence of Virgil van Dijk, Liverpool kept West Ham at arm's length and grabbed a winner five minutes from time when Diogo Jota fired home after a smart pass from Shaqiri.
Liverpool 3-2 West Ham (February 24, 2020)
Liverpool's magnificent march to the title continued at Anfield but only after they'd come from behind to beat a spirited West Ham side that ended the night still in the bottom three.
Wijnaldum's header gave the Reds a lead after just nine minutes, but rather than open the floodgates, Liverpool were rocked not once but twice as Issa Diop headed in three minutes later and Fornals put the visitors in front before the hour mark.
But with a huge shock brewing, Salah and Sadio Mane netted after 68 and 81 minutes respectively to leave the Merseysiders with a massive 22-point lead at the top and within four more wins of ending their 30-year title drought.
Last 10 meetings
Liverpool wins: 8
West Ham wins: 0
Liverpool goals: 29
Brighton goals: 9
Liverpool have been electric on the road
Liverpool have drawn four of their 10 games so far which shows they haven't exactly been perfect.
But three of those stalemates have been at Anfield where they've scored 10 and conceded five.
On the road, the Reds have been purring. Add in Champions League and Cup games and they've won seven out of eight (drawn the other) and smashed in 32 goals at an average of exactly four per match.
That's an astonishing record and, for now, they look a better bet away from home.
This could well prove their toughest test yet however, even if West Ham's form matches Liverpool's in the sense that they've also done their best work away from home.
Like Liverpool, Moyes' men have won four and drawn one of their five away encounters, while at home it's a rather mixed bag of two wins, a draw and two defeats.
Those losses came against Manchester United and Brentford, albeit only after conceding last-gasp goals in both.
In other words, West Ham are a tough nut to crack.
And yet Moyes has a miserable record against Liverpool. He's squared up to them 35 times, winning just five, drawing nine and losing 21.
Last season Liverpool were wobbling when they visited the London Stadium and yet it was the same old story for Moyes - another defeat.
So , given the way the Merseysiders are playing on their travels this term I can see a repeat on the cards.
Add in West Ham playing most of their top names in a tough, physical game on Thursday night and I'll back Liverpool (-1) on the handicap.
Jurgen Klopp's side are blasting teams on the road so backing them to win by two goals or more seems valid - especially when you see the jump in price to 15/8 from the basic win odds of 3/4
After scoring in 10 straight games for Liverpool, Salah has now drawn blanks in his last two - the home matches against Brighton and Atletico Madrid.
At the moment it seems he's enjoying the extra spaces afforded on the road and 11 of his 15 goals (in just 14 matches) this term have come away from Anfield.
That includes a hat-trick against Manchester United at Old Trafford in his last away match.
Salah has also scored five times in the four matches he's played at the London Stadium.
His price to score anytime (3/4) is worth a bet.
Salah is also second in the Premier League assists table with six to his name from 10 top-flight matches this season.
He's officially created 18 chances so there's plenty of willingness from the Egyptian to lay goals on for others too.
Planet Sport make Salah 11/4 for an assist so it's certainly another enticing offer to consider.
For West Ham, Michail Antonio has six Premier League goals and three assists too.
He's 19/10 to score anytime and 15/4 to assist in the relevant markets.
But I'll also have a small dabble on Declan Rice to assist.
The England international is more of a box-to-box midfielder for the Hammers and has three assists to his name already in the Premier League.
And yet he's a bigger price to assist (8/1) then he is to score (13/2) on Sunday despite netting just one goal in the PL this season.