Salah bagged a hat-trick and Steve Cook scored an own-goal as Liverpool hit four against Eddie Howe's side.
The Reds moved top of the Premier League - temporarily, at least, with Manchester City facing Chelsea later on Saturday - by extending their unbeaten start to the top-flight season to 16 games with an impressive display at the Vitality Stadium.
"The first one is a foul actually, but he wants to score the goal so stands on his feet and scores it".
The first came from a dubious offside call; Roberto Firmino's long range effort parried into a risky area by Asmir Begovic for Salah to slam home, though replays show the Egyptian was offside when the shot was taken.
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The goal saw Salah become the quickest player to reach 40 Premier League goals for the Reds - doing so in just 52 games - although replays showed that the Egyptian had just strayed offside when Firmino released his initial shot.
"The third goal was again brilliant".
The fourth goal arrived with 13 minutes remaining as Salah saved the best of his hat-trick until last, beating Cook to the ball and then taking his time with the finish, dribbling past Begovic twice before nonchalantly poking the ball away from two defenders on the line.
Others lauded his prolific recent form after a relatively slow start to the season, with the striker now level at the top of the Premier League scoring charts with Arsenal forward Pierre-Emerick Aubameyang. Sadio Mane is a major doubt, but Georginio Wijnaldum and Andy Robertson is back in the reckoning.
They play a high intensity, passing game, and with Liverpool's injury list growing, balancing out squad rotation while continuing to remain on the coattails of Man City will be hard.
Milner was named as the Reds' right-back for the clash at Dean Court, with Jurgen Klopp having chosen to bench his only fit orthodox right-back in Trent Alexander-Arnold ahead of Tuesday's Champions League match-up with Napoli at Anfield.