With the visitors trailing 1-0 from the first leg, Koln wasted no time in levelling the tie in a dramatic opening to proceedings.
Ondrej Duda's delivery from the left wing was superbly met by leaping Billy Goats captain Jonas Hector, who headed into the far corner to restore parity and spark a frantic opening to the game that saw four goals in a matter of minutes.
Kiel's response was immediate, as Lee Jae-sung nodded beyond Timo Horn on the follow-up to put the Bundesliga 2 outfit back in front on aggregate.
A manic, end-to-end start was then capped with two more headed goals, all inside the first 13 minutes of action, as Sebastian Andersson diverted two Florian Kainz crosses from the left into the back of the net.
Andersson's forehead was the gift that kept on giving and shortly before half-time, the 29-year-old's cushioned header was rifled home by Rafael Czichos from the edge of the home side's 18-yard box.
With Koln so ruthlessly wiping out Kiel's away-goal advantage, the hosts emerged from the break knowing they would need to score at least three times in the second period to stand any chance of earning promotion.
It was Koln, however, that went closest to adding further to the scoreline as Ioannis Gelios was tested twice in quick succession by both Duda and Kainz but the Greek goalkeeper was up to the task.
By the hour mark, Andersson had almost grabbed a third on three occasions – one effort dropping onto the crossbar and to safety after another Gelios save – as the away team continued to turn the screw.
It meant Kiel's hopes of an historic promotion were fading by the minute and it never quite managed to threaten in an attacking sense beyond Lee's early equaliser.
Koln eventually added to its lead late on courtesy of Skhiri's fine effort as they secured another season of Bundesliga football in 2020-2021, while forcing Kiel to start over again next term in its bid for a top-flight bow.