The Dutch forward scored his first goals for the Turkish club he joined earlier in the summer to propel them into the final qualifying round of the Champions League
The Romanian minnows looked nervy from the offset, and were punished after 12 minutes when Caner Erkin nodded in Gokhan Gonul’s cross from close range.
However, Vaslui produced a shock equaliser three minutes later, as Marius Niculae stabbed home a cross from Lucian Sanmartean at the far post.
Ousmane N’Doye’s penalty was saved by Volkan Demirel before Fenerbahce finally surged ahead in the 71st minute, Kuyt ripping in a powerful effort into the top corner from another Gonul pass.
The Dutch striker was not done however, and put matters beyond any doubt in the 76th minute with a simple finish after Vaslui’s defence had switched off from a free-kick.
Moussa Sow put the icing on the cake late on with an unstoppable half-volley from just outside the area and Fenerbahce now await the draw for the final qualifying round before the Champions League group stages.