The Trotters went into the game without a number of first-team regulars, including Jussi Jaaskelainen, Nicolas Anelka, El-Hadji Diouf, Kevin Nolan and Ivan Campo.
The home side enjoyed the better of the opening exchanges, with Nenad Milijas firing over when well-placed nine minutes in.
Bolton responded with Christian Wilhelmsson having a shot blocked after 20 minutes, while the visitors' backline restricting Crvena Zvezda to efforts from long range.
Ten minutes before the break Gary Speed had a half-chance following a corner from Andranik Teimourian and right on the stroke of half-time Bolton took the lead.
Teimourian's corner was only half-cleared, allowing Stelios Giannakopoulos to tee up Gavin McCann to fire home from 12 yards out.
After the restart Bolton continued to make the running, with Daniel Braaten shooting over the top, before Giannakopoulos just failed to head Teimourian's free-kick on target.
As in the first half the home side failed to trouble keeper Ali Al-Habsi with a number of strikes from distance, while Abdoulaye Meite and Lubomir Michalik maintained their dominance in defence.
With a matter of minutes left on the clock Crvena Zvezda forced a number of corners, but could not make any of them count as Bolton held on for a famous victory.
Young sub James Sinclair almost added a second goal for Wanderers deep into stoppage time, but Gary Megson's side had done enough to secure a crucial win.