The match, which kicked off at 8pm local time on Thursday, was in the eighth minute when the lights went out at Istanbul's Ataturk Olympic Stadium.
Referee Stefan Johannesson took the players off the field before the lighting was restored at around 8.20pm and the teams re-emerged for a brief warm-up before resuming the contest following a 16-minute delay.
Besiktas and Tottenham have both already secured their qualification for the knockout stages of the Europa League, but top spot is still up for grabs.
Tottenham's previous match in the competition against Partizan was also interrupted due to multiple pitch invasions at White Hart Lane.
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