Liverpool's struggling defender Sami Hyypia scored into his own net for the second game in a row to give Besiktas the lead in the 13th minute.
Bobo sidestepped Hyypia in the 82nd minute before firing home as the home side doubled their lead.
Captain Steven Gerrard's fabulous diving header five minutes from time gave Liverpool the consolation goal.
Liverpool are rooted with one point and have a daunting task to reach the knock-out stage as Besiktas moved to third with three points.
In France, Marseille kept a tightened grip on the group summit despite being held to a 1-1 draw.
Senegal forward Mamadou Niang cut ahead of his marker to poke a Djibril Cisse cross home in the 69th minute but Lucho Gonzalez pinned a 79th penalty to level the score.
Marseille have seven points from three games and Porto come second, two points less.