The American midfielder slotted home with ease after former DC United winger Andy Najar found Guillaume Gillet who set up Kljestan for a 39th minute equaliser in their eventual 3-1 loss to Olympiakos in Athens.
However, Javier Saviola scored his second of the night prior to the hour-mark after Cheikhou Kouyate was sent off for the Belgians who then saw Fabrice N'Sakala and goalkeeper Silvio Proto also given their marching orders to finish the game with eight men.
Belgian champions Anderlecht finished the group stage with just one draw and five losses from their six outings, scoring just four goals and conceding 17.
The goal was Kljestan's fourth in European competition but only his first in the Champions League proper after twice scoring in the qualifying rounds. He now has eight in all competitions so far this season with seven of those coming in the Jupiler Pro League.
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