The away side looked considerably better for long period at the Turk Telekom Arena on Tuesday and appeared destined to secure a deserved win until Yilmaz popped up to spare Gala's blushes in the 91st minute.
Both sides look set for a tough task in getting to the knockout phase after being drawn alongside Borussia Dortmund and Arsenal in Group D.
And Cesare Prandelli's side were seconds away from making that job even harder, with Dennis Praet's fine strike handing the Belgian side a deserved lead.
Aleksandar Mitrovic should have added a second a few moments later when he somehow missed the target and Yilmaz made him pay in the dying embers of the contest.
Despite the pre-match suggestion from Prandelli that the partisan support would give the Turkish giants an edge, Anderlecht refused to look overawed in the opening stages.
Chances were infrequent at both ends of the pitch during the first 20 minutes, but Besnik Hasi's men stroked the ball around confidently.
The game's first chance finally arrived in the 26th minute as Ibrahima Conte almost marked his maiden start for Anderlecht in fitting fashion.
The Guinea winger did well to latch on to Matias Suarez's lofted pass at the back post, but the 23-year-old's shot rolled just wide of the target.
Galatasaray's final ball was lacking and again Anderlecht should have capitalised in the 29th minute.
The hosts failed to deal with a Steven Defour free-kick and, after the ball landed kindly for captain Olivier Deschacht, the centre-back poked an effort straight at a grateful Fernando Muslera.
Prandelli's charges eventually stirred in the final 10 minutes of the first half and their best chance fell to Felipe Melo, who saw a low effort deflected just wide from 20 yards.
As part of a pre-planned protest against the Turkish football authorities, the home fans turned their back on proceedings for the first five minutes of the second half.
Galatasaray supporters did turn their eyes back towards the action just in time to see the first goal, although it will not have improved their collective mood.
Praet took down Defour's cross-field pass, jinked in from the left and lashed a low effort in off Muslera's right-hand post.
Mitrovic inexplicably failed to double their lead two minutes later as the Serbian skewed wide when one-on-one, while Davy Roef denied Goran Pandev with his legs a few moments later at the other end.
Galatasaray piled on the pressure in the latter stages and eventually salvaged a point as Aurelien Chedjou marched into the left side of the area and cut an inviting pass back to Yilmaz to smash home.
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