Ryan Donk put Arveladze's men ahead in the 19th minute, but their coach demanded his side immediately allow Konyaspor back in the game as Ryan Babel had been laid injured for the hosts in the build-up.
Hasan Kabze jogged through a static Kasimpasa defence to equalise from kick-off before scoring a penalty five minutes before the interval.
It proved to be the winner and Arveladze, who Kasimpasa fans voted their man of the match, was philosophical post-match.
"Anyone would make same decision as me," he said. "I decided to make this choice because this is what Kasimpasa really are.
"I talked with my guys after match and told them that I'm going to resign. Thank you very much to everybody in club."
Besiktas climbed to the top of the table with a 5-1 thumping of Kayseri Erciyesspor, banishing memories of their midweek defeat to Club Brugge in the UEFA Europa League.
Slaven Bilic's men threw away a one-goal lead to lose 2-1 in Belgium on Thursday, but Gokhan Tore had Besiktas ahead in the 25th minute at Ataturk Olympic Stadium on Saturday with a remarkable looping shot from 30 yards.
Demba Ba doubled the advantage from the spot and Olcay Sahan made it 3-0 at the break following some excellent build-up play.
Royston Drenthe smashed in a 30-yard free-kick to pull one back for the visitors, before Mustafa Pektemek bundled in Besiktas' fourth and Ramon's deflected strike made it 5-1 11 minutes from time.
The result was all the better for Besiktas, with both Galatasaray and Fenerbahce faltering in their title tilts.
Gala let a two-goal lead slip as they were held to a 2-2 home draw by Istanbul Basaksehir, while Fener lost 2-1 at Genclerbirligi.
Eskisehirspor and Rizespor eased relegation fears with much-needed victories over Mersin Idmanyurdu and Sivasspor respectively.
Basement club Balikesirsporlost 4-2 at Bursaspor, while second-bottom Karabukspor were subjected to a 5-1 thrashing at Akhisar Belediyespor.
In the weekend's remaining fixture, Gaziantepspor picked up a 2-0 victory over Trabzonspor.
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