The Reds opened up their Premier League campaign in dramatic fashion at Anfield, netting in minutes 88 and 90+4 to earn three points.
Hugo Ekitike had earlier struck on his league debut to break the deadlock, before Cody Gakpo doubled the advantage in the second half.
Antoine Semenyo, however, found the target twice to haul the Cherries back onto level terms, though the late efforts of Chiesa and Salah earned Arne Slot’s side a winning start to 2025-26.
Team
Alexis Mac Allister started for the Reds in the only change from the FA Community Shield outing last weekend.
Joe Gomez returned among the substitutes, while Ekitike, Jeremie Frimpong, Milos Kerkez and Florian Wirtz made their maiden league appearances.
Liverpool: Alisson, Van Dijk, Konate, Kerkez (Robertson, 60), Wirtz (Chiesa, 82), Szoboszlai, Mac Allister (Jones, 72), Salah, Gakpo, Ekitike (Gomez, 72), Frimpong (Endo, 60).
Unused subs: Mamardashvili, Elliott, Nyoni, Ngumoha.