Sporting threatened in the opening minute as Ali Al-Habsi had to push away a Simon Vukcevic free-kick from 20 yards, but the Trotters suffered no further alarms in the opening stages.
Portuguese striker Ricardo Vaz Te had the best chance for the visitors, lashing a shot into the sidenetting after taking down a long ball forward by Nicky Hunt.
The game then became bogged down in a midfield battle, with neither side able to forge a meaningful opening.
However, Sporting should have taken the lead on the half-hour, as Bruno Pereirinha's cross from the right was flicked on and Marat Izmailov lifted his left-foot shot over the top from five yards out at the far post.
Bolton suffered no further alarms up to half-time, but the Trotters still needed to find a breakthrough to avoid joining Everton and Spurs in making an exit from the competition.
After the restart Bolton failed to find any rhythm and rarely got within striking distance of the home goal. Pereirinha tried his luck twice from distance in the early stages, but neither effort threatened to break the deadlock.
A number of substitutions also helped make the game a scrappy affair, before Sporting came to life in the final ten minutes.
Firstly, Liedson passed up with a clear chance from 12 yards, as he drilled his shot straight at Al-Habsi when it looked easier to score after a cutback from the right left him in acres of space.
However, Pereirinha made no mistake with five minutes left to play, as a quick counter-attack sliced the Bolton rearguard wide open and the midfielder cut in from the right to curl a superb left-foot shot into the top far corner of the net from 15 yards out.
That proved to be the killer blow and there was no way back for Bolton despite three minutes of added time.