Marius Șumudică's side may have been grounded in cautious reality pre-match, but they dared to dream when Marius Niculae cancelled out Caner Erkin's 12th-minute opener. A penalty failure from Ousmane N'Doye dented their belief, however, and, with extra time looming, Fenerbahçe's counterattacking brilliance prevailed. Kuyt scored twice, before Moussa Sow wrapped up proceedings two minutes into added time.
The home side started nervously and retreated into their shell. Fenerbahçe took advantage and swamped their opponents until the pressure told, Caner heading Gökhan Gönül's neat centre past Dănuţ Coman. Vaslui fashioned an equaliser two minutes later, though, Niculae converting Lucian Sânmărtean's cross from close range.
A familiar pattern emerged as both sides traded blows, although it was the hosts who were landing marginally more of them. Nicolae Stanciu threatened, but Volkan Demirel was equal to his thunderous drive, before Mehmet Topuz's inadvertent handball led to a Vaslui penalty. Captain N'Doye froze from the spot, however, and Volkan saved comfortably.
With the hosts' confidence in tatters, Fenerbahçe turned the screw. Kuyt wasted no time in adding to their woes, unleashing an unstoppable strike from 15 metres. There was now seemingly no way back for Vaslui and the Dutch international doubled his tally on 75 minutes, following up Alex's free-kick with a calm finish.
Vaslui, who had never lost on home soil in European competition, were humbled by a fourth Fenerbahçe goal in added time when substitute Sow's blistering effort found the top corner.