The Reds were once again forced to do it the hard way against LASK Linz in Group E, but they came from a goal down to prevail 3-1 courtesy of second-half strikes from Darwin Nunez, Mohamed Salah and Luis Diaz.
Jurgen Klopp's side posted an identical triumph at Wolverhampton Wanderers - who also broke the deadlock before being put to the sword - in their most recent Premier League match, and the Reds are out to make it five league wins on the trot at Anfield.
Here, Sports Mole rounds up Liverpool's latest injury and suspension news ahead of their clash with West Ham, who also came up trumps in their Europa League opener in eerily similar fashion, coming back from a 1-0 deficit to see off Backa Topola 3-1.
Ryan Gravenberch
Status: Minor doubt
Type of injury: Cramp
Possible return date: September 24 (vs. West Ham)
Ryan Gravenberch made his first start for Liverpool at the Raiffeisen Arena on Thursday night and capped off an impressive full debut with an assist, but he was forced off with 74 minutes gone. Klopp played down the Dutchman's issue as cramp, though, and he should be fine to take his spot on the bench this weekend.
Trent Alexander-Arnold
Status: Out
Type of injury: Hamstring
Possible return date: September 27 (vs. Leicester City)
Trent Alexander-Arnold is still battling back from the hamstring injury he sustained before the international break, and Sunday's game is expected to come too soon for him, but there is a small chance that he might be available for next week's showdown with Leicester City in the EFL Cup.
Thiago Alcantara
Status: Out
Type of injury: Hip
Possible return date: October 5 (vs. Union SG)
Thiago Alcantara recently suffered a cruel setback in his recovery from a hip injury - which has sidelined him since April - and the Spaniard is thought to be unlikely to return before the start of next month.
LIVERPOOL'S SUSPENSION LIST
Liverpool have no players suspended for this match, as Virgil van Dijk makes his return from a two-game domestic ban for admitting a charge of improper conduct against Newcastle United.