Coming back into the starting line-up was a certain Mohamed Salah.
The last Liverpool player do such was Luis Suarez [now with Barcelona] against Cardiff City in March 2014, but the feat was equalled by the Egypt global who put out a five-star performance at the Vitality Stadium.
Klopp's side then doubled their advantage 3 minutes in to the second half as Salah picked up the ball in midfield and raced in to the opposition box.
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Earlier searches of Millane's accommodation at a backpackers' hostel found several items, including her passport, were missing. Beard said "that property is going to be somewhere, the clothing is going to be somewhere, we haven't found it".
He appeared to be in an offside position when the Brazilian shot, however his calm finish in to the back of the net was allowed to stand.
Things got worse for Cook, who scored an own goal to make it 3-0 to Liverpool.
Salah, who is the first Liverpool player to score three times away from home in the Premier League since Luis Suarez at Cardiff in March 2014, opened the scoring in the 25th minute before slotting twice after half-time.
But Salah and co. will be concentrating on their massive Champions League tie against Napoli on Tuesday where they need to win either 1-0 - or by two clear goals - to progress to the last-16.