Just two minutes into the game in Ankara, Fenerbahce went ahead with their first attack as captain Alex de Souza, who was involved in all the goals, delivered a killer pass for Caner Erkin to score with ease.
Fenerbahce racked up several more chances, including one effort disallowed for offside, before Cristian Baroni unleashed a fierce strike from outside the box.
Bursapor were unable to break Fenerbahce's dominance in the second half, and Brazilian Alex crossed for Semih Senturk to slot home a third from close range.
Senturk then turned provider for Alex to finish off a counter-attack in the 78th minute that sealed the game.
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