City, fielding a decent side featuring the likes of Yaya Toure, Carlos Tevez and Pablo Zabaleta, came under sustained pressure from their Turkish opponents in the first half but emerged on top as Sergio Aguero curled in the opener moments before the break.
However, it was the uncharacteristic sight of defender Kompany sprinting forward to latch on to Adam Johnson's through-ball and chip the goalkeeper that stood out after the break.
The sides were barely distinguishable as City chose to wear their new maroon away kit against Besiktas' all-red but the Istanbul side made themselves known with a series of dangerous attacks.
Ugur Boral fired over after Mustafa Pektemek drew Costel Pantilimon off his line before the goalkeeper made a fine point-blank save from Manuel Fernandes. But City led when Abdul Razak dummied Tevez's pass to set up Aguero and Kompany's fine strike settled matters before the hour mark.
Things got a little tasty after Fernandes reacted to a poor challenge from City youngster George Evans but the referee kept a lid on it despite retaliation from Alexander Kolarov.
Source: PA
Source: PA