The result kept the Ukrainians top of the group on seven points from three games, three ahead of Luxembourg who drew 1-1 at Lithuania in the section's other fixture.
Serbia's heaviest defeat as an independent nation came after coach Mladen Krstajic's adventurous 3-5-2 formation, including four attacking midfielders, backfired spectacularly.
Ukraine carved open the visiting defence almost at will and Tsygankov put the home side in the driving seat with two quick goals midway through the first half.
He opened the floodgates with a sweeping shot from 10 metres after a fine pass by right wing back Oleksandr Karavaev and doubled the lead with a thunderbolt from 20 metres into the top corner after Serbia had lost possession.
Konoplyanka netted the third barely 30 seconds into the second half, curling a neat effort past goalkeeper Marko Dmitrovic from the edge of the penalty area.
Livewire Konoplyanka made it 5-0 with what was almost a carbon copy after striker Roman Yaremchuk had scored his first international goal for Ukraine, tapping in a superb assist by Karavaev.
Only a string of good saves by Dmitrovic stopped Ukraine from scoring more goals against the hapless Serbians, who were bereft of pace and ideas in attack and looked like conceding every time the home side went forward.
Luxembourg missed a chance to complete the double over 10-man Lithuania after beating them 2-1 at home in March.
Gerson Rodrigues gave Luxembourg a 20th-minute lead before Lithuania, who had Saulius Mikoliunis sent off in the 42nd, salvaged a point thanks to an Arvydas Novikovas effort in the closing stages.
(Writing by Zoran Milosavljevic; Editing by Toby Davis)
