A double nutmeg by Naby Keita - who started on the left of Liverpool's 4-2-3-1 formation, with Firmino central and Xherdan Shaqiri on the right behind Salah - on Simon Francis and Jefferson Lerma was the highlight of an otherwise uneventful start to the game.
The Egyptian scored a ridiculous 44 goals during his debut campaign at Liverpool last season but started this campaign off slightly slower by those standards.
Liverpool showed great character to come back from behind against a plucky Burnley team midweek, but despite the good win Jurgen Klopp will be tired of Bournemouth.
Then, in the second-half, he produced a moment of magic. The forward charged towards goal and stayed on his feet as Cook attempted to trip him, before coolly dispatching a precise finish into the far bottom corner.
And during his celebrations, Salah appeared to stare back at the culprit.
His act of humility went down a storm with Liverpool fans, as did the hat-trick.
When losing in 2016, Liverpool conceded more goals in 37 minutes (four) than they have in all the other six visits to Bournemouth put together (three).
Aubameyang, who has been tremendous for Arsenal all season is alongside Aguero at 4/1 with some firms, but the Manchester City star is set to miss the clash with Chelsea later today and he could be out for a while through injury.
The England global will also miss next week's Champions League game against Napoli and the FA Cup third round game at Wolves.