An unfamiliar Wanderers line-up struggled to gel early on and it was little surprise when they went behind after just seven minutes, as Ailton took advantage of some sloppy defending.
Mexico striker Jared Borgetti fired Bolton level just before the half-hour and Sam Allardyce's men then wasted a number of good opportunities to clinch maximum points.
Allardyce made seven changes to the side that lost 5-1 to Chelsea, with Tal Ben Haim, Abdoulaye Faye, Radhi Jaidi and El-Hadji Diouf the only survivors from the starting line-up at Stamford Bridge.
They began like a set of strangers as Besiktas applied the early pressure. Ex-Manchester United midfielder Kleberson created a great chance for Ailton after just four minutes, but he could not find the target with his header.
The former Werder Bremen striker made no mistake three minutes later after Ben Haim played Joey O'Brien into trouble and the youngster lost possession to Tumer Metin.
He played the ball through to Ailton and the Brazilian smashed his shot beyond the helpless Ian Walker.
Khalilou Fadiga almost levelled in the 20th minute as Bolton began to find their feet, but home goalkeeper Oscar Cordoba just managed to tip his powerful drive over the crossbar.
The visitors hit back in the 29th minute when Borgetti finished from a teasing Diouf cross, to remind Allardyce of his potential to be a first-team regular.
With their confidence boosted Wanderers controlled the rest of the first half and Hidetoshi Nakata and Diouf both squandered chances to give them the lead.
The second half started at a great pace and Ibrahim Akin began to cause the visitors real problems. He fired over from distance just after the restart and then saw two efforts blocked.
Besiktas did not have it all their own way and Cordoba had to be alert to rush off his line and dispossess Ricardo Gardner. Cordoba should have had more to do but poor final balls from Diouf and Nakata prevented Wanderers creating much danger.
Diouf thought he'd put the Trotters ahead when he slotted the ball home 20 minutes from full-time, but the Senegal forward had carelessly strayed offside.
The match degenerated into a scrappy affair late on, but that suited Bolton as they secured a valuable away point to put them on the road to qualification for the knockout stages.