The fixture had already been played back in December, with the hosts winning 2-1, but was marred by two bizarre incidents.
Kasimpasa's Dutch defender Ryan Donk threw a second ball into the penalty area to put off Besiktas forward Hugo Almeida as he prepared to take a shot on goal, and a home supporter also ran onto the field in an attempt to attack Besiktas midfielder Manuel Fernandes.
Following a review from the Turkish Football Federation, it was declared that match official Baris Simsek made an error in not awarding Besiktas a penalty and failing to dismiss Donk for the transgression, and ordered a re-match.
There was a vastly different outcome second time around, too, with the visitors racing into a three-goal lead before the break.
Almeida gained revenge from the initial fixture by giving his side the lead in the 26th minute when he tapped home into an empty net from six yards.
Pedro Franco doubled the lead eight minutes later, poking the ball home from close range after Atiba Hutchinson's header from a corner rebounded kindly off the back of Veli Kavlak.
And it was Kavlak who put the result beyond doubt a minute before the interval, nodding home after Olcay Sahan's initial header had been blocked.
Serdar Kurtulus was dismissed four minutes into the second half for a second bookable offence but it mattered little as Besiktas comfortably held on, the result cementing Slaven Bilic's side's position in third place in the table, five points behind leaders Fenerbahce.
