The same applied to their hosts who were winless in their last three matches and having lost 5-1 against Atletico Madrid in their last UCL assignment.
Ekitike returns to Eintracht
Eintracht had scored 17 goals in their last six matches in all competitions before facing the Reds, but had also conceded 19 in the same time frame, indicating a devastating attack but porous defence.
A lot of pre-match chatter centred around Hugo Ekitike's swift return to the club, which sold him to the Premier League giants in the summer, and whether his performance would be affected as a result, should he be selected by Arne Slot.
Mo Salah's omission for the second successive Champions League game was a big call and huge surprise from the Dutchman, and the first time since the Egyptian King joined the club in 2017 that this scenario had occurred.
A subdued start from both teams didn't see an awful lot in the way of goalmouth action, until Alexander Isak's two shots on target in the eighth and tenth minutes, both saved well by Eintracht keeper, Michael Zetterer.
Germans strike first
The Bundesliga outfit had barely had an attack before former Leeds ace, Rasmus Kristensen, found himself all alone at the back post and able to drill his shot past Giorgi Mamardashvili.
Another game without a clean sheet for the Reds might've been a worry for Slot, as 16 of their last 18 matches in all competitions had seen Liverpool's opponents score at least once.
However, with 77.4% possession leading up to the half hour mark, it appeared to be just a matter of time before the visitors were back on terms.
Fate would decree that Ekitike would be the man to silence the Deutsche Bank Park crowd, the striker taking advantage of acres of space left by an attacking Eintracht to outpace the home defence and collect Andrew Robertson's long ball before coolly slotting home.
The goal gave him the unique honour of being the first player in Eintracht history to both score for and against them in European competition.
Set-piece magic from Liverpool
Soon after, the hosts were left to rue their marking at corners, with Virgil van Dijk rising highest to power home a bullet header on 38, before Ibrahima Konate did exactly the same from the opposite side in the 44th minute.
Van Dijk's scoring contribution was his 26th headed goal out of the 30 he's scored for Liverpool, with all five of his Champions League goals also coming via his head.
Only Harry Kane (34) has more headed goals for one club in the Premier League.
A fifth goal conceded in the final 15 minutes of the first-half placed the Germans at the top of the tree in that particular UCL metric, suggesting that Dino Toppmoller's side need to tighten up as they approach the break in games.
Dominik Szoboszlai's influence on proceedings had been clear for all to see throughout the first half, with a pass completion of 98% (54 successful from 55 attempted), as well as providing the assist for Konate's goal.
The Hungarian would go on to add a late goal himself, completing a fine night's work for him personally.
Isak hooked at half-time
The same can't be said for Isak who was hooked at half-time and continues to struggle after his big-money move from Newcastle.
After his two early chances he did little to impress in an attacking sense, and his 66.7% pass completion was comfortably the worst on show from any outfield player in both teams.
His replacement, Federico Chiesa, soon got into the action with an off-target effort, sandwiched between Ekitike's blocked shot and Florian Wirtz's half-chance.
The Reds continued on the front foot with three more attempts at goal before Cody Gakpo fired home a fourth from Wirtz's first competitive assist of his Liverpool career - discounting the one in the Community Shield.
Four goals scored for the first time in a UCL game since November 2024 against Bayer Leverkusen would've been a pleasing aspect of the win for the Reds' management team, as would Wirtz's second assist to Szoboszlai five minutes later.
As with Isak, the young German has taken a while to adapt to life at Anfield, though this was one of his better games and should give him confidence moving forward.
His winning back of possession on seven separate occasions was the joint most from a Liverpool point of view, as was his seven touches in the Eintracht box.
Curtis Jones the architect behind Liverpool's win
A flurry of late substitutions from the Reds allowed Slot to rest players ahead of a difficult trip to West London on Saturday to face Brentford and their old captain, Jordan Henderson.
Salah had 15 minutes in which to impress, and three shots (of which two were on target during that cameo) suggested he did just that. The blow to his ego by not starting was clearly a masterstroke from his manager.
With Liverpool attempting 699 total passes in the game, it was their most since the start of last season, with Curtis Jones deserving the plaudits for his contribution in this regard.
The combative midfielder's 127 passes were at least 17 more than any other player on the pitch, and the successful completion of 122 of them gave Jones a stunning 96.1% completion, the best individual stat on the night.
He was also involved in the most one-on-one duels (nine) and won the joint most (five) in what turned out to be a convincing argument from him to be kept in the team as a starter for the next set of matches.
Check out the match summary here.
