Souza scored twice to give Fenerbahce a 2-0 advantage in the first leg of their round-of-32 Europa League tie against Lokomotiv Moscow in Istanbul on Tuesday night.
The first real chance of the game was created in the 13th minute when Robin van Persie hit the ball on the volley from point blank range, but his shot was punched away by goalkeeper Guilherme.
The deadlock was broken five minutes later when Souza's header nestled into the left side of the net after he connected to Gokhan Gonul's cross in the box.
After taking the lead, Vitor Pereira's side began to find their stride and had the majority of the possession, but they failed to make their chances count, and in turn allowed Lokomotiv to get more of a stranglehold on the game.
The Russian outfit managed to get numerous crosses into Fenerbahce's box, but the quality on the ball was missing and the visitors entered the half-time interval with a one-goal deficit.
After the break, Guilherme was called upon to make a crucial stop after Volkan Sen unleashed a well-struck long-range effort at goal, but the keeper managed to keep the ball out of the left side of the net.
At the other end, Nemanja Pejcinovic got a sniff as he moved to the edge of the penalty area before drilling a shot towards the bottom left corner, but Fabiano made the save.
Van Persie had two decent opportunities in quick succession - the first shot went wide and the second was thwarted by Lokomotiv's defence after the striker broke free.
Following a spell of pressure, Fenerbahce doubled their lead as Souza controlled Caner Erkin's cross into the box with his first touch before hammering the ball into the back of the net.
Lokomotiv struggled to find a response and they return to Russia with a two-goal deficit.